  Let $H$ be a Hopf algebra over a commutative ring $k$ with unity and
$\sigma:H\otimes H\longrightarrow k$ be a cocycle on $H$. In this paper, we
show that the Yetter-Drinfeld module category of the cocycle deformation Hopf
algebra $H^{\sigma}$ is equivalent to the Yetter-Drinfeld module category of
$H$. As a result of the equivalence, the "quantum Brauer" group BQ$(k,H)$ is
isomorphic to BQ$(k,H^{\sigma})$. Moreover, the group $\Gal(\HR)$ constructed
in \cite{Z} is studied under a cocycle deformation.
