From Character Sheaves to Characters of Deligne–Lusztig Representations via Categorical Traces

A very important result of Lusztig asserts that characters of Deligne–Lusztig representations are obtained by the sheaf-to-function correspondence from character sheaves. The goal of my talk is to outline a proof of a generalization of this result using the categorical trace machinery. This is a joint work in progress with Dennis Gaitsgory and Nick Rozenblyum.