  The main result of the present paper is that the stable and unstable
C*-algebras associated to a mixing Smale space always contain nonzero
projections. This gives a positive answer to a question of the first listed
author and Karen Strung and has implications for the structure of these
algebras in light of the Elliott program for simple C*-algebras. Using our main
result, we also show that the homoclinic, stable, and unstable algebras each
have real rank zero.
