Description
When a group G acts properly on a tree T, it is a classical result that the action of G on the Gromov compactification X of the tree is amenable, i.e. the crossed product C(X)xG is nuclear. We will introduce an analogue of the crossed product C-algebra C(X)xG in the context of fundamental C-algebras of graph of C-algebras (Fima,Freslon 2013). This C-algebra has interesting features which leads to new proofs of results concerning approximation properties and KK-theory.
