Lusztig's classification divides the representation theory of G(Fq) (G a reductive algebraic group) in to its semisimple and unipotent parts in analogy to the Jordan decomposition. I will explain a refinement of this idea in the geometric setting. Namely, we will exhibit the collection of categorical representations of the reductive group G (over the complex numbers) as sheaf over the moduli of semisimple conjugacy classes in the dual group, whose fibers may be understood as unipotent representations for a smaller reductive group. One motivation is to study the cohomology of G(C)-character varieties of surfaces and its relations with the representation theory of G(Fq). This is joint work with David Ben-Zvi.