The fundamental lemma for Hecke algebras in large positive characteristic

Langlands and Shelstad conjectured that the fundamental lemma should hold for the full Hecke algebra.  By a global argument based on the trace formula, in characteristic zero, their conjecture is a consequence of the fundamental lemma proved by Ngo Bau Chau, We show that the fundamental lemma for the full spherical Hecke algebra also holds in large positive characteristic. The proof is based on a twisted version of a Kato-Lusztig formula and other "twisted" results in the representation theory of complex reductive groups.

This is joint work with Bill Casselman and Jorge Cely.