A Cuntz-Pimsner model for the C⁎-algebra of a graph of groups

Abstract

We provide a Cuntz-Pimsner model for graph of groups C⁎-algebras. This allows us to compute the K-theory of a range of examples and show that graph of groups C⁎-algebras can be realised as Exel-Pardo algebras. We also make a preliminary investigation of whether the crossed product algebra of Baumslag-Solitar groups acting on the boundary of certain trees satisfies Poincaré duality in KK-theory. By constructing a K-theory duality class we compute the K-homology of these crossed products.