But there seems to be little doubt that the YPG is leading the fight. Its flags flutter over the checkpoints along the newly liberated rural roads and at the military bases closest to the front lines. Its graffiti is scrawled over the walls of the captured towns and villages, as in Tal Saman, where the initials “YPG” were spray-painted alongside the pledge to take Raqqa.

The Kurdish-Arab alliance, with U.S. assistance, plans to recruit and train an additional 10,000 Arab fighters for an offensive on Raqqa, said Rojda Felat, one of the commanders of the offensive to encircle the city. But YPG participation will be essential “because we have proved that we are the most effective fighters,” she said.

“We will even go past Raqqa,” she added, to other areas farther south controlled by the Islamic State, which is also known as ISIS, ISIL or Daesh.

Whether it is wise to send an overwhelmingly Kurdish force to capture the overwhelmingly Arab city of Raqqa is in question, however. A Kurdish push on Raqqa risks alienating the local population, perhaps encouraging residents who otherwise would not support the Islamic State to fight on its behalf, according to Abu Issa, a commander with the rebel Free Syrian Army’s Liwa Thuwar al-Raqqa, or Raqqa Revolutionaries Brigade.

“We saw in Iraq and other places that if the local people are not involved in the liberation, there won’t be any stability,” he said in an interview at his headquarters, in a remote farmhouse in the countryside of Raqqa province. He and his group are from Raqqa, and though they are loosely allied with the SDF, they fly the flag of the Free Syrian Army.

“All the Arabs know that the SDF are YPG, and if things continue as they are, there will be big problems in the future, sectarian clashes and conflict,” Abu Issa said. “People don’t understand why the YPG are going to Raqqa. It’s an entirely Arab area, and the Arabs feel marginalized.”