  In the early 1990s, Borcea-Voisin orbifolds were some of the ear- liest
examples of Calabi-Yau threefolds shown to exhibit mirror symmetry. However,
their quantum theory has been poorly investigated. We study this in the context
of the gauged linear sigma model, which in their case encom- passes
Gromov-Witten theory and its three companions (FJRW theory and two mixed
theories). For certain Borcea-Voisin orbifolds of Fermat type, we calculate all
four genus zero theories explicitly. Furthermore, we relate the I-functions of
these theories by analytic continuation and symplectic transfor- mation. In
particular, the relation between the Gromov-Witten and FJRW theories can be
viewed as an example of the Landau-Ginzburg/Calabi-Yau correspondence for
complete intersections of toric varieties.
