GCR and CCR groupoid $C*$-algebras Lisa Clark 46L0546L35locally compact groupoidC*-algebraHilbert module Suppose $G$ is a second countable, locally compact, Hausdorff groupoid 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 $G^0/G$ 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 $G^0/G$ is a $T_0$ topological space and all of the isotropy groups are GCR. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.2955 10.1512/iumj.2007.56.2955 en Indiana Univ. Math. J. 56 (2007) 2087 - 2110 state-of-the-art mathematics http://iumj.org/access/