MATCHING THEOREMS FOR TWISTED ORBITAL INTEGRALS

Let F be a rho-adic field and E a cyclic extension of F of degree d co rresponding to the character kappa of F-x. For Any positive integer m, we consider H = GL(m, E) as a subgroup of G = GL(md,F). In this paper we discuss matching of orbital integrals between H and G. Specificall y, ordinary orbital integrals corresponding to regular semisimple elem ents of H are matched with orbital integrals on G which are twisted by the character kappa. For the general situation we only match function s which are smooth and compactly supported on the regular set. If the extension E/F is unramified, we are able to match arbitrary smooth, co mpactly supported functions.