We outline an approach to proving functoriality of automorphic
representations using trace formula. More specifically, we construct a family
of integral operators on the space of automorphic forms whose eigenvalues are
expressed in terms of the L-functions of automorphic representations and begin
the analysis of their traces using the orbital side of the stable trace
formula. We show that the most interesting part, corresponding to regular
conjugacy classes, is nothing but a sum over a finite-dimensional vector space
over the global field, which we call the Steinberg-Hitchin base.