Analytic continuation of better-behaved GKZ systems and Fourier-Mukai transforms

We study the relationship between solutions to better-behaved GKZ hypergeometric systems near different large radius limit points, and their geometric counterparts given by the \(K\)-groups of the associated toric Deligne-Mumford stacks. We prove that the \(K\)-theoretic Fourier-Mukai transforms associated to toric wall-crossing coincide with analytic continuation transformations of Gamma series solutions to the better-behaved GKZ systems, which settles a conjecture of Borisov and Horja.