The K-theory of maximal and reduced Roe algebras for Hecke pairs with equivariant coarse embeddings

TL;DR

This paper extends K-theoretic analysis to Roe algebras associated with Hecke pairs, establishing isomorphisms and proving the Baum--Connes conjecture in this setting.

Contribution

It generalizes the Dirac-dual-Dirac method to Hecke pairs with equivariant coarse embeddings, linking maximal and reduced Roe algebras.

Findings

K-theoretic isomorphisms between maximal and reduced Roe algebras for Hecke pairs

Extension of Baum--Connes conjecture proof to this context

Generalization of Dirac-dual-Dirac method to Hecke pairs

Abstract

In this paper, we generalize the Dirac-dual-Dirac method to Hecke pairs with equivariant coarse embeddings and establish the K-theoretic isomorphisms between the maximal and reduced equivariant Roe algebras. We also extend these results to prove the Baum--Connes conjecture in this context.