Subfactors associated to compact Kac algebras

We construct inclusions of the form (B0⊗P)G⊂(B1⊗P)G, whereG is a compact quantum group of Kac type acting on an inclusion of finite dimensional C*-algebrasB0⊂B1 and on aII1 factorP. Under suitable assumptions on the actions ofG, this is a subfactor, whose Jones tower and standard invariant can be computed by using techniques of A. Wassermann. The subfactors associated to subgroups of compact groups, to projective representations of compact groups, to finite quantum groups, to finitely generated discrete groups, to vertex models and to spin models are of this form.