GCR and CCR Groupoid C*-algebras

Suppose G is a second countable, locally compact, Hausdorffgroupoid with a fixed left Haar system. Let G 0 /G denote the orbit space of G and C*(G) denote the groupoid C*-algebra. Suppose that the isotropy groups of G are amenable. We show that C*(G) is CCR if and only if G°/G is a T 1 topological space and all of the isotropy groups are CCR. We also show that C*(G) is GCR if and only if G° /G is a To topological space and all of the isotropy groups are GCR.