Intermediate subalgebras for reduced crossed products of discrete groups

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