Equivalence bundles over a finite group and strong Morita equivalence for unital inclusions of unital $C^*$-algebras

Let $\mathcal{A}= \{A_t \}_{t \in G}$ and $\mathcal{B}= \{B_t \}_{t\in be $C^*$-algebraic bundles over a finite group $G$. $C=\oplus_{t G}A_t$ $D=\oplus_{t\in G}B_t$. Also, let $A=A_e$ $B=B_e$, where $e$ is the unit element in We suppose that $C$ $D$ are unital $A$ $B$ have elements $D$, respectively. In this paper, we shall show if there an equivalence $\mathcal{A}-\mathcal{B}$-bundle $G$ with some properties, then inclusions of $C^*$-algebras $A \subset C$ $B D$ induced by $\mathcal{A}$ $\mathcal{B}$ strongly Morita equivalent. saturated $A' \cap C= \mathbf{C} 1$. equivalent, automorphism $f$ bundle $\mathcal{A}-\mathcal{B}^f $-bundle $\mathcal{B}^f$ $f$, which defined $\mathcal{B}^f = \{B_{f(t)} G}$. Furthermore, give application.