Abstract
We construct the crossed product [Formula: see text] of a C(X)-algebra [Formula: see text] by an endomorphism ρ, in such a way that ρ becomes induced by the bimodule [Formula: see text] of continuous sections of a vector bundle ℰ → X. Some motivating examples for such a construction are given. Furthermore, we study the C*-algebra of G-invariant elements of the Cuntz-Pimsner algebra [Formula: see text] associated with [Formula: see text], where G is a (noncompact, in general) group acting on ℰ. In particular, the C*-algebra of invariant elements with respect to the action of the group of special unitaries of ℰ is a crossed product in the above sense. We also study the analogous construction on certain Hilbert bimodules, called "noncommutative pullbacks".
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