Coactions of a finite-dimensional C*-Hopf algebra on unital C*-algebras, unital inclusions of unital C*-algebras and strong Morita equivalence

Let A and B be unital C*-algebras and let H be a finite-dimensional C*-Hopf algebra. Let H-0 be its dual C*-Hopf algebra. Let (rho, u) and (sigma, v) be twisted coactions of H-0 on A and B, respectively. In this paper, we show the following theorem: Suppose that the unital inclusions A subset of A (sic)rho,u H and B subset of B (sic)sigma,v H are strongly Morita equivalent. If A' boolean AND (A (sic)rho,u H) = C1, then there is a C*-Hopf algebra automorphism lambda(0) of H-0 such that the twisted coaction (rho, u) is strongly Morita equivalent to the twisted coaction ((id(B) circle times lambda(0)) circle sigma, (id(B) circle times lambda(0) circle times lambda(0))(v)) induced by (sigma,v) and lambda(0).