Classification and realizations of type III factor representations of   Cuntz-Krieger algebras associated with quasi-free states
  We completely classify type III factor representations of Cuntz-Krieger algebras associated with quasi-free states up to unitary equivalence. Furthermore, we realize these representations on concrete Hilbert spaces without using GNS construction. Free groups and their type ${\rm II}_{1}$ factor representations are used in these realizations. 
Katsunori Kawamura