  In recent papers, a model of a two-sheeted spacetime M4XZ2 was introduced and
the quantum dynamics of massive fermions was studied in this framework. In the
present study, we show that the physical predictions of the model are perfectly
consistent with observations and most important, it can solve the puzzling
problem of the four-dimensional localization of the fermion species in
multidimensional spacetimes. It is demonstrated that fermion localization on
the sheets arises from the combination of the discrete bulk structure and
environmental interactions. The mechanism described in this paper can be seen
as an alternative to the domain wall localization arising in continuous five
dimensional spacetimes. Although tightly constrained, motions between the
sheets are, however, not completely prohibited. As an illustration, a resonant
mechanism through which fermion oscillations between the sheets might occur is
described.
