STRONG MORITA EQUIVALENCE FOR INCLUSIONS OF C*-ALGEBRAS INDUCED BY TWISTED ACTIONS OF A COUNTABLE DISCRETE GROUP

We consider two twisted actions of a countable discrete group on sigma-unital C*-algebras. Then by taking the reduced crossed products, we get two inclusions of C*-algebras. We suppose that they are strongly Morita equivalent as inclusions of C*-algebras. Also, we suppose that one of the inclusions of C*-algebras is irreducible, that is, the relative commutant of one of the sigma-unital C*-algebra in the multiplier C*-algebra of the reduced twisted crossed product is trivial. We show that the two actions are then strongly Morita equivalent up to some automorphism of the group.