2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102044In another article we associated a dynamical system to a non-properly ordered Bratteli diagram. In this article we describe how to compute the $K-$group $K_0$ of the dynamical system in terms of the Bratteli diagram. In the case of properly ordered Bratteli diagrams this description coincides with what is already known, namely the so-called dimension group of the Bratteli diagram. The new ordered group defined here is more relevant for non-properly ordered Bratteli diagrams. We use our main result to describe $K_0$ of a substitutional system.13 pages;definition of $ΔZ^..$ used in Lemma 3.7 appeared after the proof of the Lemma. This is attended to now. A little more clarity in 3.10Dynamical Systems37B10, 54H20text