Covariant Fields of $C^*$-Algebras under Rieffel Deformation

We show that Rieffel's deformation sends covariant $\mathcal{C}(T)$-algebras into $\mathcal{C}(T)$-algebras. We also treat the lower semi-continuity issue, proving that Rieffel's deformation transforms covariant continuous fields of $C^*$-algebras into continuous fields of $C^*$-algebras. Some examples are indicated, including certain quantum groups.