Riesz bases of exponentials on unbounded multi-tiles

We prove the existence of Riesz bases of exponentials of L^2(Omega), provided that Omega in R^d is a measurable set of finite and positive measure, not necessarily bounded, that satisfies a multi-tiling condition and an arithmetic property that we call admissibility. This property is satisfied for any bounded domain, so our results extend the known case of bounded multi-tiles. We also extend known results for submulti-tiles and frames of exponentials to the unbounded case.