Realization of rigid C*-bicategories as bimodules over type II$_1$ von Neumann algebras

We prove that every rigid C*-bicategory with finite-dimensional centers (finitely decomposable horizontal units) can be realized as Connes bimodules over finite direct sums of II$_1$ factors. In particular, we realize every multitensor C*-category as bimodules over a finite direct sum of II$_1$ factors.