The whole region is a mishmash of ethnic, linguistic, social and religious groups. In many cases the origin of nations (as in peoples, not countries) are social groups or religions rather than ethnicity or language.

The Kurds are, generally, speaking a Iranian language and are descended from a social group rather than an ethnicity. The term Kurd seems to originally have referred to nomadic or semi-nomadic Iranians, although it seems to have been a mix of Turkic origins as well.

Thus the definition of the Kurds were that they were a group of nomads mainly of Iranian descent, but with Turkic roots mixed in, who mainly spoke Kurdish, an Iranian language. This group slowly progressed from being a linguistic and social group to being an ethnic one. To say exactly when and how is very difficult, but by the early Medieval era, most seem to have recognised the Kurds as a people. As to why they do not have a state, it is very complex. There are lots of groups in the region that do not have their own state, historically or otherwise.

The Kurds did dominate the two late Medieval tribal confederacies of the Black Sheep (Qara Koyunlu) and White Sheep (Ak Koyunlu), the latter which would spawn the Safavid dynasty that would rule Persia for more than two hundred years.

The Kurds have been unlucky in that they have been at the crossroads of more powerful Empires and states that have conquered them and being divided by the victors of ww1 drawing new borders in the Middle East.

Could you clarify what you mean by "a pawn"?