Bounded trace C*-algebras and integrable actions

Let G be a second countable group, A be a separable C*-algebra with bounded trace and a strongly continuous action of G on A. Suppose that the action of G on induced by is free and the G-orbits are locally closed. We show that the crossed product A×G has bounded trace if and only if G acts integrably (in the sense of Rieffel and an Huef) on . In the course of this, we show that the extent of non-properness of an integrable action gives rise to a lower bound for the size of the (finite) upper multiplicities of the irreducible representations of the crossed product.Mathemactics Subject Classification (1991): 46L55