  Let G be a connected reductive group defined over a finite field F_q and let
L be the Levi subgroup (defined over F_q) of a parabolic subgroup P of G. We
define a linear map from class functions on L(F_q) to class functions on
G(F_q). This map is independent of the choice of P. We show that for large q
this map coincides with the known cohomological induction (whose definition
involves a choice of P).
