  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 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.
