In the article of Lusztig (1977) I'm reading, about representation theory of finite Chevalley groups, after introducing unipotent representations, and the Deligne-Lusztig Variety $X_w$, there are some results related to the number of rational points on a variety and eigensvalues/eigenspaces of $F^\delta$, with $\delta$ chosen such that $F^\delta$ acts trivially on $W$.
Is there any reference explaining how the eigenspaces/eigenvalues are related to the study of unipotent representation ? Because to me, it seems to appear out of nowhere, and I'm not sure why the author is doing that.
