A new look at the proof of $K$-theoretic amenability for groups acting on trees

Abstract

We generalize the construction by Pytlik and Szwarc of uniformly bounded representations for free groups to groups acting on trees. We deduce a new version of the proof (by Alain Valette and the author, 1983) of the fact that locally compact groups acting on trees with amenable stabilizers are amenable in $K$-theory.