ISTANBUL — For almost two years, Syrian Kurds, with American weapons, air cover and training, have fought and died in battle against the Islamic State. They have taken pride in their status as the United States’ most faithful proxy in the fight against the militant group, and they have hoped their effectiveness as warriors would lead to American support for Kurdish political gains inside Syria.

So, many Kurds shuddered when Turkish tanks and soldiers recently rolled into northern Syria, with American support, to push back against Kurdish gains. They saw it, perhaps prematurely, as a replay of a century of betrayal by world powers, going back to the end of World War I, when they were promised, then denied, their own state in the postwar settlement.

“The Kurds are going to scream betrayal at every turn when they think things are not going to go their way, because they’ve had a century of it,” said Joost Hiltermann, the program director for the Middle East and North Africa at the International Crisis Group, and a longtime expert on the Kurds.

The Syrian Kurds say their aim is to establish an autonomous region, not their own state, where their rights are protected, in whatever settlement comes from the long Syrian civil war. And they say they hope that the United States will support them in that desire.