We construct an I-function of the projective bundle P(V) associated with a
not necessarily split vector bundle V\to B as a Fourier transform of the
S^1-equivariant J-function of the total space of V and show that it lies on the
Givental Lagrangian cone of P(V). Using this result, we show that the quantum
cohomology D-module of P(V) splits into the direct sum of copies of the quantum
cohomology D-module of the base space B. This has applications to the
semisimplicity of big quantum cohomology.Comment: 36 pages, 1 figur