Integrable actions and transformation groups whose C*-algebras have bounded trace

Let (G,X) be a locally compact transformation group. We characterize when the associated transformation-group C*-algebra C-0 (X) x G has bounded trace. If G acts freely on X, then C-0(X) x G has bounded trace if and only if the action of G on CO(X) is integrable. If G is abelian and the stability subgroups vary continuously, then C-0(X) x G has bounded trace if and only if the action is integrable relative to the stability subgroups. The upper multiplicity of an irreducible representation of C-0 (X) x G is invariant under the dual action of (G) over cap; as an application we identify the largest bounded-trace ideal in Type I transformation-group C*-algebras.