  In this paper, we introduce a C*-algebra associated to any substitution (via
its Bratteli diagram model). We show that this C*-algebra contains the partial
crossed product C*-algebra of the corresponding Bratteli-Vershik system and
show that these algebras are invariant under equivalence of the Bratteli
diagrams. We also show that the isomorphism class of the algebras, together
with a distinguished set of generators, is a complete invariant for equivalence
of Bratteli diagrams.
