I will give a brief overview of the theory of traces in higher categories and explain how this gives a new
approach to the study of representation of finite groups of Lie type. Given an algebraic group G over a finite
field F_q, I will explain how representations of G(F_q) arise as traces of categorical representations of G.
Moreover, I will explain the higher categorical origin of Deligne-Lusztig representations and give a new
conceptual computation of their characters which explains their regularity as a function of q. This is joint
work with Gaitsgory and Varshavsky.