  To a proper inclusion N\subset M of II_1 factors of finite Jones index [M:N],
we associate an ergodic C*-action of the quantum group S_\mu U(2). The
deformation parameter is determined by -1<\mu<0 and [M:N]=|\mu+\mu^{-1}|. The
higher relative commutants can be identified with the spectral spaces of the
tensor powers of the defining representation of the quantum group.
  This ergodic action may be thought of as a virtual subgroup of S_\mu U(2) in
the sense of Mackey arising from the tensor category generated by M regarded as
a bimodule over N. \mu is negative as M is a real bimodule.
