2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163478In this paper, we introduce a $C^{\ast}$-algebra associated with a proper primitive substitution. We show that the $C^{\ast}$-algebra is simple and purely infinite and contains the associated Cuntz-Krieger algebra and the crossed product $C^{\ast}$-algebra of the corresponding Cantor minimal system. We calculate the $K$-groups.19 pagesOperator AlgebrasDynamical Systemstext