Shifts on the HyperfiniteII1Factor

R. T. Powers has constructed a family of unital endomorphisms of the hyperfiniteII1factorR. The range of each Powers shiftσis a subfactor of index 2 inR. A cocycle conjugacy invariant for a Powers shift is its commutant index, i.e., the first index k for which the range ofσkhas a nontrivial relative commutant inR. Previously we have shown that all Powers shifts of commutant index 2 are cocycle conjugate. In this paper results are obtained on the classification of the cocycle conjugacy classes of Powers shifts of higher commutant index.