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 (M-i) 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+root 13/2, 12 + 3 root 13, 4 + root 13, 11+3 root 13/2, 13+3 root 13/2, 19+5 root 13/2, 7+root 13/2}. 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. (C) 2013 Elsevier Inc. All rights reserved.