A quantum Leray–Hirsch theorem for banded gerbes

For a gerbe $\mathcal{Y}$ over smooth proper Deligne–Mumford stack $\mathcal{B}$ banded by finite group $G$, we prove structure result on the Gromov–Witten theory of $\mathcal{Y}$, expressing invariants in terms twisted various flat $U(1)$‑gerbes $\mathcal{B}$. This can be viewed as Leray–Hirsch type for gerbes.