Perverse sheaves, base change homomorphism and fundamental lemma of Jacquet and Ye.

We give a geometric interpretation of the base change homomorphism between the Hecke algebra of GL(n) for an unramified extension of local fields of p ositive characteristic. For this, we use some results of Ginzburg, Mirkovic and Vilonen related to the geometric Satake isomorphism. We give a new pro of of these results in the positive characteristic case. By using that geometric interpretation of the base change homomorphism, we prove the fundamental lemma of Jacquet and Ye for arbitrary Hecke function in the equal characteristic case. (C) Elsevier, Paris.