On a family of C*-subalgebras of Cuntz–Krieger algebras

In this paper, we study a family of C*-subalgebras defined by fixed points of generalized gauge actions of a Cuntz–Krieger algebra by introducing a family of étale groupoids whose associated C*-algebras are these C*-subalgebras. We show that topological conjugacy classes of one-sided topological Markov shifts are characterized in terms of the isomorphism classes of these étale groupoids.