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We prove that given any compact group  G , there exists a minimal action of  G  on a II 1  factor  M  such that the bimodule category of the fixed-point II 1  factor  M G   is naturally equivalent with the representation category of  G . In particular, all subfactors of  M G   with finite Jones index can be described explicitly.

The representation category of any compact group is the bimodule category of a II 1 factor