Cross products of strongly Morita equivalent 𝐶*-algebras

Suppose that a locally compact group G G acts on strongly Morita equivalent C ∗ {C^ * } -algebras A A and B B and let A ⋊ G A G and B ⋊ G B G denote the corresponding crossed products. We present conditions which imply that A ⋊ G A G and B ⋊ G B G are also strongly Morita equivalent and we apply our result to improve upon known theorems concerning strong Morita equivalence between certain transformation group C ∗ {C^ * } -algebras.