  Expanding the classical work of Kazhdan-Lusztig, we construct a bar
involution and canonical bases on the $q$-Brauer algebra introduced by Wenzl.
We define explicit actions of the $q$-Brauer algebra on the tensor spaces, and
formulate $\imath$Schur dualities between the $q$-Brauer algebra and the
$\imath$quantum groups of type AI and AII respectively.
