Quantum group-twisted tensor products of C -algebras. II

For a quasitriangular C -quantum group, we enrich the twisted tensor product constructed in the first part of this series to a monoidal structure on the category of its continuous coactions on C -algebras. We define braided C -quantum groups, where the comultiplication takes values in a twisted tensor product. We show that compact braided C -quantum groups yield compact quantum groups by a semidirect product construction.