JUDY WOODRUFF: In the war to drive ISIS from northern Syria, an unlikely group has emerged: the stateless Kurdish people. Split across territories of four Middle Eastern nations, ethnic Kurds have long endured repression, discrimination, even genocide. But today, they form the backbone of the U.S.-backed Syrian Democratic Forces. It's a group American leaders call the greatest warriors fighting the Islamic State.
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GEN. JOSEPH DUNFORD, Chairman, Joint Chiefs of Staff: They are the most effective force we have right now and a force we need to go in Raqqa.
GEN. RAYMOND THOMAS, U.S. Special Operations Command: That's the ghost force, that has just taken, you know, is half way through Raqqa and has taken every march objective we've had so far.
BRETT MCGURK, Special Presidential Envoy: They also have never lost a battle.
JUDY WOODRUFF: Their unusual mix of Marxist ideology, local governance and military prowess has made them a sort of political Rorschach test. Labels describing them span the political spectrum: pro-Western fighters, radical leftists, hardcore Marxists, atheists, revolutionary feminists, among others. Not open to debate: their central role in defeating ISIS.
Gayle Tzemach Lemmon reports.
GAYLE TZEMACH LEMMON: Klara from Raqqa, the only name she'll use, has spent years in battle, leading soldiers and devising strategy. But now the world is watching.
KLARA FROM RAQQA, Syrian Democratic Forces Commander (through interpreter): The fight is very hard but we have hope that we will win.
GAYLE TZEMACH LEMMON: But now, the world is watching, as the fight against ISIS closes in on its makeshift capital, Klara's own hometown of Raqqa. She is part of the Kurds' own all-women fighting force, known in Kurdish as the YPJ. They have fought and died right alongside their brothers-in-arms. And some of the most celebrated fighters, including snipers, come from their ranks.
She took us to Raqqa's front line, to the site of a still- smoking is car bomb attack. She described a brutal fight: landmines and booby traps, snipers and suicide attacks.
KLARA FROM RAQQA (through interpreter): They know they are surrounded and can't survive.
GAYLE TZEMACH LEMMON: Her forces, she says, draw strength from the unique and turbulent history of the Kurdish people.
KLARA FROM RAQQA (through interpreter): It's revenge, for the atrocities and injustices that the Kurds suffered in the past. Out of our experiences grew a soul of resistance and struggle to achieve legitimate rights and fight against injustice.
GAYLE TZEMACH LEMMON: It's a deeply personal fight for these young women soldiers.
ARVEEN, YPJ Soldier (through interpreter): Raqqa was the capital of ISIS. They bought and sold Kurdish women here. And we want to tell them that the Kurdish women can protect themselves. And YPJ will take revenge, for all Kurdish women.
CANFIDA, YPJ Soldier (through translator): All the fighting and liberating we are doing now, it is for the new generation. It is not only for the Kurds. It will strengthen our identity and history. We are writing our own history, now.
FAWZA YOUSEIF, Democratic Federalism of Northern Syria (through interpreter): The Kurdish revolution is a women's revolution.
GAYLE TZEMACH LEMMON: Fawza Youseif works for the leading Kurdish party in Syria. For them, this is more than just a war. It's an opportunity, to lead and to govern after years without their rights.
Have you been waiting for this moment?
FAWZA YOUSEIF (through interpreter): Syrian Kurds from the beginning were more organized and politically conscious. When the revolution begun, Kurdish society was ready.
GAYLE TZEMACH LEMMON: But other actors have also sought advantage in Syria's civil war vacuum. Not least, from the north: Turkish President Recep Tayyip Erdogan.
PRESIDENT RECEP TAYYIP ERDOGAN, Turkey (through interpreter): If our allies are sincere in their fight against the Islamic State, we are ready to act together with them.
GAYLE TZEMACH LEMMON: Embroiled in decades-long conflict with his own Kurdish population, Erdogan sees Syrian Kurds as one and the same enemy. And Kurdish ties across the Syria-Turkey border are strong. In northern Syria, the streets are flush with posters of Turkey's president's main opponent: Abdullah Ocalan. The Kurdish leader jailed in Turkey is a hero to Syrian Kurds, the founding father of their socialist ideology.
Fearing rising regional influence for the Kurds, Turkey's president has launched air attacks on Kurdish forces in Syria — forces the U.S. is backing — and he's threatened to do more, clashing specifically over the northern city of Manbij.
PRESIDENT RECEP TAYYIP ERDOGAN (through interpreter): Manbij belongs to Arabs. It does not belong to Kurdish leaders. We relayed this to our American friends. We told the Americans that Kurdish fighters must not stay there. The Americans always reply: they have withdrawn, or they are withdrawing, but they haven't withdrawn yet.
GAYLE TZEMACH LEMMON: And it doesn't stop there. The Turkish government has also built close ties with Kurds in Iraq, dividing Kurds among themselves. In a controversial referendum scheduled for next month, Iraqi Kurds will vote on an independent state. The Kurds in Syria hope not to be left behind.
Cementing political gains is what Syrian Kurds say must come next for them. They have long sought to govern themselves. And finally, Fawza Youseif says, they may have that chance.
FAWZA YOUSEIF (through interpreter): The Kurds had a dream, to have freedom and rights in their own land. And now to have a chance at this land, where we can live together, with freedom and democracy, it's a very big chance.
GAYLE TZEMACH LEMMON: She spends her days planning the future of local governance. Kurdish language, Kurdish and Arab leadership together, local decisions; all are part of what they call a new secular and democratic project here.
SIPAN CHATO, Rojava University (through interpreter): It's opened our eyes. If a rock is on a flower, it will take time to grow. But if you take the rock off, it will flourish. The war allowed the people to raise their head.
GAYLE TZEMACH LEMMON: And allowed them to take their revolutionary ideas into government, says Sipan Chato, vice dean of the faculty of science at newly established Rojava University.
Government offices already have both male and female leaders. Representation of ethnic minorities is a priority, and local councils are responsible for making local decisions. But despite the lofty rhetoric, opponents have leveled heavy charges. Some say the Kurds now in power tolerate little opposition. That it's their way, or no way.
ABDULKARIM HUSAIN MUHAMMAD, Kurdistan Democratic Party of Syria: We cannot live under their democracy.
GAYLE TZEMACH LEMMON: Abdulkarim Husain Muhammad leads a Kurdish opposition party. We met him in his office in Erbil, Iraq. He's been jailed three times he said, by leaders of Yousief's party, on charges he calls false and politicized.
ABDULKARIM HUSAIN MUHAMMAD (through interpreter): Their room is the room of the jail cell. This is where the opposition meets. Everything is forbidden when you say no to them. Everything must be their color, their ideology, their philosophy.
GAYLE TZEMACH LEMMON: Others charge that Kurdish fighters have furthered ethnic divisions, even pushing Arab civilians deeper into ISIS territories. What's more, many today accuse the Kurds of a de-facto, if uneasy, alliance with the regime of Syrian President Bashar al Assad. While Assad leaves the Kurds to govern themselves, critics charge, the Kurds have avoided directly confronting him.
In the Kurdish city of Qamishli, in far northeastern Syria, Assad's flags and posters still hang. In Kobani, a war-torn city on the Turkish border, we met a proud military dad.
Muhammad Abdi's daughter Miriam has been injured twice fighting ISIS. And she's back on the frontlines today. He said he hopes that all his daughter's friends, lost in battle, will not have died for nothing.
MUHAMMAD ABDI, Daughter Wounded Fighting ISIS (through interpreter): This is a critical moment, because we've already lost so many. If we don't get our rights after losing all these people, then when we will get them?
GAYLE TZEMACH LEMMON: And how many more lives will be lost on the way to an answer?
For the PBS NewsHour, I'm Gayle Tzemach Lemmon in northern Syria.