Morita context of weak Hopf algebras

Let H be a finite-dimensional weak Hopf algebra and A a left H-module algebra with its invariant subalgebra AH. We prove that the smash product A # H is an A-ring with a grouplike character, and give a criterion for A # H to be Frobenius over A. Using the theory of A-rings, we mainly construct a Morita context 〈AH, A#H, A, A, τ, μ〉 connecting the smash product A # H and the invariant subalgebra AH, which generalizes the corresponding results obtained by Cohen, Fischman and Montgomery.