C∗-ALGEBRAS ASSOCIATED WITH THE FUNDAMENTAL GROUPS OF GRAPHS OF GROUPS

Abstract. We construct nuclear C∗-algebras associated with the fundamental groups of graphs of groups of finite type. It is well-known that every word-hyperbolic group with zero-dimensional boundary, in other words, every group acting trees with finite stabilizers is given by the fundamental group of such a graph of groups. We show that our C∗-algebras are ∗-isomorphic to the crossed products arising from the associated boundary actions and are also given by Cuntz-Pimsner algebras. We also compute the K-groups and determine the ideal structures of our C∗-algebras. 1