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Symmetry types of bands in solids are specified by means of band representations of space groups. This is a new kind of representation that corresponds to bands of energies rather than to single energies as in the case of usual representations. It is shown that each band representation defines a symmetry type of a band by specifying the symmetry of localized orbitals with respect to a whole lattice of point group centers. In this symmetry specification the quasicoordinate q in the Wigner-Seitz cell plays a similar role to what is played by the quasimomentum k in the symmetry specification of Bloch states in the Brillouin zone.
J. Žák (Sun,) studied this question.