The Picard groups of unital inclusions of unital $C^{\ast }$-algebras induced by involutive equivalence bimodules

Let $A$ be a unital $C^{\ast }$-algebra and $X$ an invulutive $A-A$-equivalence bimodule. Let $A\subset C_X$ be the unital inclusion of unital $C^{\ast }$-algebras induced by $X$. We suppose that $A^{\mathrm{\prime }}\cap C_X=\mathbf{C}1$. We shall compute the Picard group of the unital inclusion $A\subset C_X$.