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We give a formula of the framed one-leg orbifold Gromov-Witten vertex wherethe leg is gerby with isotropy group $\bZ_m$. Then we use this formula tocompute the Gromov-Witten invariants of the local $\cB\bZ_m$ gerbe. We willalso compute some examples of the degree 1 and degree 2 $\bZ_2$-Hodgeintegrals.

A Formula of the One-leg Orbifold Gromov-Witten Vertex and Gromov-Witten Invariants of the Local $\cB\bZ_m$ Gerbe