Locally unitary groupoid crossed products Geoff Goehle 47L6522A22groupoidscrossed products We define the notion of a principal $S$-bundle where $S$ is a groupoid group bundle and show that there is a one-to-one correspondence between principal $S$-bundles and elements of a sheaf cohomology group associated to $S$. We also define the notion of a locally unitary action and show that the spectrum of the crossed product is a principal $\hat{S}$-bundle. Furthermore, we prove that the isomorphism class of the spectrum determines the exterior equivalence class of the action and that every principal bundle can be realized as the spectrum of some locally unitary crossed product. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4143 10.1512/iumj.2011.60.4143 en Indiana Univ. Math. J. 60 (2011) 411 - 442 state-of-the-art mathematics http://iumj.org/access/