On a family of $C^{\ast }$-subalgebras of Cuntz-Krieger algebras

In this paper, we study a family of $C^{\ast }$-subalgebras defined by fixed points of generalized gauge actions of a Cuntz-Krieger algebra, by introducing a family of 'etale groupoids whose associated $C^{\ast }$-algebras are these $C^{\ast }$-subalgebras. We know that topological conjugacy classes of one-sided topological Markov shifts are characterized in terms of the isomorphism classes of these 'etale groupoids.