Non-unipotent representations and categorical centres

Abstract: Let G be a connected reductive group defined over a finite field F_q. We give a parametrization of the irreducible representations of G(F_q) in terms of (twisted) categorical centres of various monoidal categories associated to G. (Results of this type were known earlier for unipotent representations. Analogous results for the parametrization of character sheaves on G were also known earlier.)