  Let $H$ be a finite Hopf algebra with $C_{H,H} = C_{H,H}^{-1}.$ The duality
theorem is shown for $H$, i.e., $$ (R # H)# H^{\hat *} \cong R \otimes (H \bar
\otimes H^{\hat *}) \hbox {as algebras in} {\cal C}.$$ Also, it is proved that
the Drinfeld double $(D(H),[b])$ is a quasi-triangular Hopf algebra in ${\cal
C}$.
