  We give a formula of the framed one-leg orbifold Gromov-Witten vertex where
the leg is gerby with isotropy group $\bZ_m$. Then we use this formula to
compute the Gromov-Witten invariants of the local $\cB\bZ_m$ gerbe. We will
also compute some examples of the degree 1 and degree 2 $\bZ_2$-Hodge
integrals.
