Base change fundamental lemma for Bernstein centers of principal series blocks

Abstract

Let $G$ be an unramified group over a $p$-adic field $F$. This article introduces a base change homomorphism for the Bernstein center of a principal series block, and proves that two functions related by this base change homomorphism are associated. This result provides new evidence for the conjecture on twisted endoscopic transfer of the stable Bernstein center proposed by T. Haines, which will be applied to a general conjecture on test functions for Shimura varieties due to R. Kottwitz and T. Haines.