Intermediate subalgebras for reduced crossed products of discrete groups

Let: A be an action of a discrete group on a unital C*-algebra A by *-automorphisms and let A, denote the corresponding reduced crossed product C*-algebra. Assuming that satisfies the approximation property, we establish a sufficient and (almost always) necessary condition on the action for the existence of a Galois correspondence between intermediate C*-algebras for the inclusion A A, and partial subactions of. This condition, which we refer to as pointwise residual proper outerness, is a natural noncommutative generalization of freeness.