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

We construct a nuclear C*-algebra associated with the fundamental group of a graph 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*-algebra is *-isomorphic to the crossed product arising from the associated boundary action and is also given by a Cuntz-Pimsner algebra. We also compute the K-groups and determine the ideal structures of our C*-algebras.