Twisted Partial Actions, A Classification of Stable C*-Algebraic Bundles (Preliminary Version)

We introduce the notion of continuous twisted partial actions of a locally compact group on a C*-algebra. With such, we construct an associated C*-algebraic bundle called the semidirect product bundle. Our main theorem shows that, given any C*-algebraic bundle which is second countable and whose unit fiber algebra is stable, there is a continuous twisted partial action of the base group on the unit fiber algebra, whose associated semidirect product bundle is isomorphic to the given one.