Gromov-Witten invariants of toric fibrations

We prove a conjecture of Artur Elezi [4] in a generalized form suggested by Givental [5]. Namely, our main result relates genus-0 Gromov-Witten invariants of a bundle space with such invariants of the base, provided that the fiber is a toric manifold. When the base is the point, a new proof of mirror theorems by A. Givental [6] and H. Iritani [10] for toric manifolds is obtained.