The bimodules of finite Jones index over a II1 factor, equipped with the Connes tensor product, form a fusion algebra. Using techniques of Popa, I will present the first explicit computations of fusion algebras for a family of II1 factors defined by generalized Bernoulli actions and identify them with extensions of Hecke fusion algebras. We obtain in particular the first explicit examples of II1 factors without non-trivial finite index bimodules and hence, without non-trivial finite index subfactors.