They do, which is why Kurds becoming a majority, in, say, the military, let alone as part of the general population would be so disastrous for Turkey. The Kurds have been fighting the Turks for independence on-again off-again for centuries, and the current conflict in eastern Turkey has been going on for more then three decades and claimed tens of thousands of lives.
http://en.wikipedia.org/wiki/Timeline_of_Kurdish_uprisings
http://en.wikipedia.org/wiki/Kurdish%E2%80%93Turkish_conflict
The Kurds seem to look a bit different than the Turks.