On the representations of disconnected reductive groups over F_q

Let \hat G be the semidirect product of a connected reductive group G over F_q with a finite cyclic group generated by a quasisemisimple automorphism of G defined over F_q. In this paper we prove a conjecture of G. Malle concerning the extensions of unipotent representations of G(F_q) to \hat G(F_q).