Base change for Bernstein centers of depth zero principal series blocks

Abstract

Let $G$ be an unramified group over a $p$-adic field. This article introduces a base change homomorphism for Bernstein centers of depth-zero principal series blocks for $G$ and proves the corresponding base change fundamental lemma. This result is used in the approach to Shimura varieties with $\Gamma_1(p)$-level structure initiated by M. Rapoport and the author in [HR2].