Let $A$ and $B$ be unital $C^*$-algebras and $H$ a finite dimensional $C^*$-Hopf algebra with its dual $C^*$-Hopf algebra $H^0$. Let $(\rho, u)$ and $(\sigma, v)$ be twisted coactions of $H^0$ on $A$ and $B$, respectively. Le $C=A\rtimes_{\rho, u}H$ and $D=B\rtimes_{\sigma, v}H$ and let $C_0 =C\rtimes_{\widehat{\rho}}H^0$ and $D_0 =D\rtimes_{\widehat{\sigma}}H^0$