  In this paper we describe the C*-algebras associated to the Baumslag-Solitar
groups with the ordering defined by the usual presentations. These are Morita
equivalent to the crossed product C*-algebras obtained by letting the group act
on its directed boundary. We use the method of categories of paths to define
the algebras, and to deduce the presentation by generators and relations. We
obtain a complete description of the Toeplitz algebras, and we compute the
K-theory of the Cuntz-Kreiger algebras.
