  We present here the K-theoretic version of mirror models of toric manifold.
First, we recall the construction of cohomological mirrors for toric manifolds,
i.e. representations of the toric hypergeometric functions from quantum
cohomology theory by complex oscillating integrals. Then we repeat the
construction in the K-theoretic situation, and obtain complex oscillating
integrals representing q-hypergeometric functions from quantum K-theory of
toric manifolds, bundles, and super-bundles. Finally, we examine the Lagrangian
varieties parameterized by critical points of the phase functions of these
oscillating integrals.
