  We prove the Effros-Hahn conjecture for groupoid algebras with coefficients
in a sheaf, obtaining as a consequence a description of the ideals in skew
inverse semigroup rings. We also use the description of the ideals to
characterize when the groupoid algebras with coefficients in a sheaf are von
Neumann regular, primitive, semiprimitive, or simple. We apply our results to
the topological dynamics of actions of inverse semigroups, describing the
existence of dense orbits and minimality in terms of primitivity and
simplicity, respectively, of the associated algebra. Moreover, we apply our
results to the usual complex groupoid algebra of continuous functions with
compact support, used to build the C*-algebra associated with a groupoid, and
describe criteria for its simplicity.
