Appears in collection : 2025 - T1 - WS2 - Tempered representations and K-theory

The goal of this talk is a simple, concrete description of the topological K-theory of the reduced C*-algebra of a reductive p-adic group $G$, in terms coming from representation theory.

We will discuss the structure of several group algebras of $G$, and how the K-theory can be computed from the space of irreducible tempered $G$-representations. The final description is closely related to conjectures by Aubert-Baum-Plymen-Solleveld.