Coverings of directed graphs and crossed products of C*-algebras by coactions of homogeneous spaces

We show that if p : F → E is a covering of directed graphs, then the Cuntz-Krieger algebra C* (F) of F can be viewed as a crossed product of C* (E) by a coaction of a homogeneous space for the fundamental group π1(E). Combining this result with information about Cuntz-Krieger algebras gives some interesting corollaries which suggest conjectures about crossed products by coactions of homogeneous spaces of discrete groups. We then prove these conjectures.