Affine buildings, tiling systems and higher rank Cuntz-Krieger algebras

To an r-dimensional subshift of finite type satisfying certain special prop erties we associate a C*-algebra A. This algebra is a higher rank version o f a Cuntz-Krieger algebra. In particular, it is simple, purely infinite and nuclear. We study an example: if Gamma is a group acting freely on the ver tices of an (A) over tilde(2), building, with finitely many orbits, and if Omega is the boundary of that building, then C (Omega) x Gamma is the algeb ra associated to a certain two dimensional subshift.