Strong Morita equivalence for inclusions of C^*-algebras induced by twisted actions of a countable discrete group - Kodaka, Kazunori (Mathematica Scandinavica, 2021)
We consider two twisted actions of a countable discrete group on σ-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 σ-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.