  We consider "cubes" in products of finite cyclic groups and we study their
tiling and spectral properties. (A set in a finite group is called a tile if
some of its translates form a partition of the group and is called spectral if
it admits an orhogonal basis of characters for the functions supported on the
set.) We show an analog of a theorem due to Iosevich and Pedersen, Lagarias,
Reeds and Wang, and the third author of this paper, which identified the tiling
complements of the unit cube in Euclidean space with the spectra of the same
cube.
