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A graph of groups consists of an undirected graph with each edge and vertex assigned a group. There is a one-to-one correspondence between graphs of groups and group actions on trees. In this way, the study of graphs of groups is equivalent to the study of group actions on trees. In 2017, Brownlowe, Mundey, Pask, Spielberg and Thomas developed a generators and relations construction of a C∗-algebra associated to a graph of groups, which they linked to a specific crossed-product C∗-algebra to show that the correspondence between graphs of groups and group actions on trees extends to their r...

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. ⁎ ⁎ Open Access Status Volume