SAKAWIYA, Syria — The body of a dead, bearded ISIS fighter lay beside the road as we left the front-line village of Sakawiya on Saturday in a convoy guided by a senior Kurdish fighter. With the support of the United States, Arab and Kurdish troops launched this operation last week to cut the supply lines of the self-proclaimed Islamic State (ISIS) near the Turkish border at a town called Manbij.

So far, ISIS is resisting with artillery, snipers and rocket fire, but it is slowly losing village by village under pressure from heavy coalition airstrikes. Local combatants say ISIS wants to hold this position at all costs. In the past, it has been able to smuggle in about 500 fighters a month across the Syrian-Turkish border in this area. “They use it for transferring weapons, bullets and fighters,” said Abdo Muslim, an Arab fighter from the town of Serrin. “They don’t want to lose it.”“So far, we didn’t face each other directly,” Munzir Eris, a young Kurdish fighter told The Daily Beast, “only rockets, artillery and snipers. [But] since yesterday we have taken six villages.”

The fog of war is complicated here by the fog of politics.

For the last two years, the most effective forces fighting ISIS on the ground in this region have come from the YPG, the Kurdish People’s Protection Units that Ankara says are closely tied to the PKK, the Kurdistan Workers’ Party, that has waged a decades-long war against the Turkish government. And for most of this war on the self-proclaimed Islamic State caliphate, Ankara has treated the Kurds as a greater threat to its interests than ISIS.

The fact that the U.S. has thrown its weight behind the Kurdish fighters by deploying U.S. Special Forces advisors among them, some of whom wear YPG badges, has complicated efforts to coordinate the offensive with Ankara.

So the question of who is leading this fight—Syrian Arabs or the Kurds of the YPG—has become extremely sensitive. Turkish President Recep Tayyip Erdogan said Thursday that Turkish intelligence is watching closely to make sure Arabs “will be the main force in the operation.”

The Americans are taking the same position: “The Syrian Arabs are leading the operation and have more than 2,000 fighters in the operation. The Kurds have approximately 500 supporting the operation,” Col. Chris Garver, a spokesperson for the U.S.-led coalition told The Daily Beast. “This does not discount Kurdish contributions. … But to say the Kurds are leading the Manbij operation is inaccurate.”

On the ground in Syria it is, frankly, difficult to see whether this is true or not.

From the Syrian town of Kobani, where I am based, it seems Kurdish fighters of the YPG dominate the fight. On May 30, already, the first Kurdish reinforcements were deployed and now Kobani is saddened by regular funeral marches for those who’ve died in this operation. Last Thursday four Kurdish fighters were buried, and on Saturday eight fighters were buried who were killed in an ISIS rocket attack. But senior Kurdish officials assure me that mostly Arab fighters are involved in this operation in order to calm Turkey’s concerns about the increased Kurdish-U.S. cooperation.Although the U.S. says it supports the Arabs as part of the Kurdish-led Syrian Democratic Forces (SDF) with training and weapons, local Arabs say the support is limited and that they haven’t seen any training. “We ask the international community to provide us with more weapons to defeat ISIS,” Abdo Muslim said.

In order to embrace the several elements joined together here, the offensive is being conducted in the name of the Manbij Military Council.Meanwhile, it is becoming increasingly difficult to visit front lines after a local photographer took pictures showing U.S. Special Forces with patches of Kurdish fighters, angering Turkey and the U.S.

Although Kurdish officials initially were happy with the pictures, they slowly realized it could compromise the fight against ISIS and now see the photos as a public relations disaster.

“This campaign is dependent on politics,” Munzir Eris, a young Kurdish fighter, told The Daily Beast. “It is a very sensitive campaign and any wrong behavior could lead to problems.” So far it seems the operation has at least tacit approval from Turkey due to U.S. pressure and guarantees that Arabs will be in charge.

“The operation is dominated for 60 per cent by Arabs and 40 per cent by Kurds, Turkmen and other ethnic groups,” Mohamed Abu Amdil, an Arab commander of the Manbij military council assured The Daily Beast. “Of course Turkey will accept liberating Manbij, because just the [Arab] people of Manbij will protect their city.”Salih Haji Mohammed, the Kurdish deputy and co-chair of the Manbij city council set up at the beginning of April says the council strives for good relations with Turkey. “In our social contract, we say we want to have good relations with neighboring countries like Turkey. Any country that does not interfere in Manbij and our areas, we will have good relations with,” he said. Such as statement is rare. Normally, Syrian Kurdish officials are hostile towards Turkey and accuse the Turks of supporting ISIS and massacring Kurds in Turkey.Although the Kurds have been accused of ethnic cleansing of Arabs and Turkmen, on the ground it seems that civilians welcome both Kurdish and Arab fighters by singing, kissing them on the cheeks and throwing away the dark veils they were forced to wear by ISIS.“The Kurdish soldiers liberated our village and brought us here,” said Behiste Fawaz, 48, a displaced Arab civilian in a makeshift IDP camp near Tisreen dam, who begged reporters and fighters for cigarettes. “We have never seen in the world such injustice. I wish ISIS fighters die like dogs in the wild and I wish God destroys them,” she said.Other Arab civilians were even more vocal as we talked under a burning sun.

“They kill us, they slaughter us, they cut our hands and legs,” said Mustafa Aloush, who is originally from the village of Halula. “We are in hell. Even Israel didn’t do this to us, Israel is merciful compared to ISIS,” he told The Daily Beast.“Under their control, I couldn’t smoke, they insulted us and forced us to wear clothes as women.” He pointed at his feet, showing how he was forced to wear his pants above his ankles. “All the people support the fighters, my God help you,” he told me. Another Arab woman from a village occupied by ISIS started spontaneously to curse ISIS as I recorded her on video, but she changed her mind quickly and begged me not to publish the video. “I am afraid of ISIS, they will slaughter my sons,” she said.Local officials reject the reports suggesting the Kurds drive out Arabs. Mansour Saloum, a senior Arab official from Tal Abyad and a leader of the Kurdish project to set up a federal region in northern Syria, rejected such claims. “The people who will drive out ISIS from the town are people from Manbij,” he said.Senior Arab officials and civilians living in the self-administered areas led by Kurds often get annoyed when I ask them about accusations by the Syrian activist group Raqqa Is Being Slaughtered Silently, based in Turkey, that accuse Kurds of driving out Arabs from their villages, and claim Arabs in Raqqah are joining ISIS to defend themselves against Kurds.“Why do journalists always ask these sectarian questions?” Sheikh Farouk al-Mashi, a former member of the Syrian parliament, wanted to know. He will lead the Arab-dominated Manbij city council after the town is liberated from ISIS. “I have a Syrian ID, and Kurds have a Syrian ID. Let those people who talk against us in Turkey and Europe come here and fight ISIS. Why this distortion in media about problems between Kurds and Arabs?”

Meanwhile more than 50,000 Iraqi Sunni Arabs are expected to flee to the Kurdish-led areas in northern Syria to escape the coming battle for Mosul, across the frontier in Iraq, according to the UN Refugee Agency (UNCHR). Already, 4,266 Iraqi refugees are living in the al-Hol refugee camp under dire conditions awaiting international support. Most of the aid given to the Kurds, thus far, as been for making war, not supporting those displaced by it.

The campaign to take Manbij will most likely last weeks. “Taking these villages is easy,” Abdo Muslim said. “But taking Manbij is difficult. It’s a big city and a needs a lot of work,” he added. “The frontlines are wide, and they [ISIS] are not withdrawing.”