  Let ${\mathfrak g}$ be a finite dimensional complex semisimple Lie algebra.
The finite dimensional representations of the quantized enveloping algebra
$U_q({\mathfrak g})$ form a braided monoidal category $O_{int}$. We show that
the category of finite dimensional representations of a quantum symmetric pair
coideal subalgebra $B_{c,s}$ of $U_q({\mathfrak g})$ is a braided module
category over an equivariantization of $O_{int}$. The braiding for $B_{c,s}$ is
realized by a universal K-matrix which lies in a completion of $B_{c,s}\otimes
U_q({\mathfrak g})$. We apply these results to describe a distinguished basis
of the center of $B_{c,s}$.
