  We introduce a global Landau-Ginzburg model which is mirror to several toric
Deligne-Mumford stacks and describe the change of the Gromov-Witten theories
under discrepant transformations. We prove a formal decomposition of the
quantum cohomology D-modules (and of the all-genus Gromov-Witten potentials)
under a discrepant toric wall-crossing. In the case of weighted blowups of
weak-Fano compact toric stacks along toric centres, we show that an analytic
lift of the formal decomposition corresponds, via the
$\widehat{\Gamma}$-integral structure, to an Orlov-type semiorthogonal
decomposition of topological $K$-groups. We state a conjectural functoriality
of Gromov-Witten theories under discrepant transformations in terms of a
Riemann-Hilbert problem.
