Representations of the Cuntz - Krieger algebras . II — Permutative representations —

We generalize permutative representations of the Cuntz algebras for the Cuntz-Krieger algebra OA for any A. We characterize cyclic permutative representations by notions of cycle and chain, and show their existence and uniqueness. We show necessary and sufficient conditions for their irreducibility and equivalence. In consequence, we have a complete classification of permutative representations of OA for any A. Furthermore we show that the uniqueness of irreducible decomposition holds for permutative representation and decomposition formulae.