Multi-tiling and Riesz bases

Let S be a bounded, Riemann measurable set in R^d, and L 
be a lattice. By a theorem of Fuglede, if S tiles R^d with         
translation set L, then S has an orthogonal basis of exponentials. 
We show that, under the more general condition that S multi-tiles  
R^d with translation set L, S has a Riesz basis of exponentials. The
proof is based on Meyer's quasicrystals. This is a joint work with 
Nir Lev.