  Let $H$ and $L$ be quantum groupoids. If $H$ has a quasitriangular structure,
then we show that $L$ induces a Hopf algebra $C_{L}(L_s)$ in the category
$_{H}\mathcal{M}$, which generalizes the transmutation theory introduced by
Majid. Furthermore, if $H$ is commutative, we can construct a Hopf algebra
$C_H(H_s)_F$ in the category $_H\mathcal{M}_F$ for a weak invertible unit
2-cocycle $F$, which generalizes the results in \cite{D83}. Finally, we
consider the relation between two Hopf algebras: $C_H(H_s)_F$ and
$C_{\widetilde H}(\widetilde{H}_s)$, and obtain that they are isomorphic as
objects in the category $_{\widetilde H}\mathcal{M}$, where $(\widetilde H,
\widetilde{\mathcal{R}})$ is a new quasitriangular quantum groupoid induced by
$(H, \mathcal{R})$.
