I do know that the Kurds were promised a Kurdistan even well before the last scene of Lawrence of Arabia.
Those were presumably the Kurds living in the former Ottoman Empire.
They're Iranian by blood. They just didn't take a liking to the Shia faith when most of Ancient Persia decided to embrace it.
They complain about the Turks now, but it was entirely their decision to break off from the rest of Iran and join the Ottomans.
I wish them well. But they themselves take some blame for their problems. They keep trusting the wrong people. America has never had any serious interest in supporting a Kurdish state.