Let $S$ be an smooth algebraic surface and $C$ be a smooth curve, both over $\mathbb{C}$. Assume that a finite group $G$ acts on $S$ and $C$ respectively and the induced acting of $G$ on $S\times C$ has no fixed point. I now want to compute $NS((S\times C)/G)$. Is it true that $NS((S\times C)/G)\cong NS(S\times C)^G$ as abelian groups?