We introduce a new notion of twisted actions of inverse semigroups and showthat they correspond bijectively to certain regular Fell bundles over inversesemigroups, yielding in this way a structure classification of such bundles.These include as special cases all the stable Fell bundles. Our definition of twisted actions properly generalizes a previous oneintroduced by Sieben and corresponds to Busby-Smith twisted actions in thegroup case. As an application we describe twisted etale groupoid C*-algebras interms of crossed products by twisted actions of inverse semigroups and showthat Sieben's twisted actions essentially correspond to twisted etale groupoidswith topologically trivial twists.
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