Morita invariants of quasitriangular comodule algebras

We use representations of braid groups of Coxeter types BC and D to produce invariants of representation categories of quasitriangular comodule algebras. Such categories form a prevalent class of braided module categories. This is analogous to how representations of braid groups of Coxeter type A produce invariants of representation categories of quasitriangular Hopf algebras, a prevalent class of braided monoidal categories. This work also includes concrete examples, and classification results for $K$-matrices of quasitriangular comodule algebras.