Tensor C∗-categories arising as bimodule categories of II1 factors

We prove that if C is a tensor C∗-category in a certain class, then there exists an uncountable family of pairwise non stably isomorphic II1 factors (Mi) such that the bimodule category of Mi is equivalent to C for all i. In particular, we prove that every finite tensor C∗-category is the bimodule category of a II1 factor. As an application we prove the existence of a II1 factor for which the set of indices of finite index irreducible subfactors is {1,5+132,12+313,4+13,11+3132,13+3132,19+5132,7+132}. We also give the first example of a II1 factor M such that Bimod(M) is explicitly calculated and has an uncountable number of isomorphism classes of irreducible objects.