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

Key Points

• The aim is to generalize the Dirac-dual-Dirac method to Hecke pairs and establish relationships in K-theory.
• Generalized the Dirac-dual-Dirac method for Hecke pairs with equivariant coarse embeddings.
• Established K-theoretic isomorphisms between maximal and reduced Roe algebras.
• Extended results to prove the Baum-Connes conjecture within this framework.
• Demonstrated new K-theoretic isomorphisms between different types of Roe algebras.
• Showed applicability of the generalized method to Hecke pairs.
• Proved Baum-Connes conjecture in the context of equivariant coarse embeddings.