Invariants for Normal Completely Positive Maps on the Hyperfinite $II_1$   Factor
  We investigate certain classes of normal completely positive (CP) maps on the hyperfinite $II_1$ factor $\mathcal A$. Using the representation theory of a suitable irrational rotation algebra, we propose some computable invariants for such CP maps. 
Debashish Goswami, Lingaraj Sahu