Author’s abstract: 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 \(\mathcal{O}_{\mathrm{int}}\). We show that the category of finite dimensional representations of a quantum symmetric pair coideal subalgebra \(B_{\mathrm{c,s}}\) of \(U_q(\mathfrak{g})\) is a braided module category over an equivariantization \(\mathcal{O}_{\mathrm{int}}^{(\sigma)}\) of \(\mathcal{O}_{\mathrm{int}}\). The braiding for \(B_{\mathrm{c,s}}\) is realized by a universal K-matrix which lies in a completion of \(B_{\mathrm{c,s}}\otimes U_q(\mathfrak{g})\). We appply these results to describe a distinguished basis of the center of \(B_{\mathrm{c,s}}\).