Cyclically ordered group and C^*-dynamical system

Let G be a group equipped with a cyclic order such that G be a cyclically ordered group. Under the given order and a particular condition on G, the positive cone P(G) of G is a cyclically ordered semigroup. We induced the representation of a C ^*-algebra A in a Hilbert space such that we obtain a covariant representation of an action of P(G) by automorphism of A. C ^*-dynamical system (A, α, P(G)), where α is an action of P(G) by automorphism of A. (paper)