  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.
