The K-group of substitutional systems

In 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 K0 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 group defined here is more relevant for non-properly ordered Bratteli diagrams. We use our main result to describe K0 of a substitutional system.