  We introduce a new notion of twisted actions of inverse semigroups and show
that they correspond bijectively to certain regular Fell bundles over inverse
semigroups, 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 one
introduced by Sieben and corresponds to Busby-Smith twisted actions in the
group case. As an application we describe twisted etale groupoid C*-algebras in
terms of crossed products by twisted actions of inverse semigroups and show
that Sieben's twisted actions essentially correspond to twisted etale groupoids
with topologically trivial twists.
