We associate to each symplectic 4-orbifold \(X\) a canonical smooth symplectic resolution \(\pi: \tilde{X}\rightarrow X\), which can be done equivariantly if \(X\) comes with a symplectic \(G\)-action by a finite group. Moreover, we show that the resolutions of the symplectic 4-orbifolds \(X/G\) and \(\tilde{X}/G\) are in the same symplectic birational equivalence class; in fact, the resolution of \(\tilde{X}/G\) can be reduced to that of \(X/G\) by successively blowing down symplectic \((-1)\)-spheres.
To any finite symplectic \(G\)-action on a 4-manifold \(M\), we associate a pair \((M_G,D)\), where \(\pi: M_G\rightarrow M/G\) is the canonical resolution of the quotient orbifold and \(D\) is the pre-image of the singular set of \(M/G\) under \(\pi\). We propose to study the group action on \(M\) by analyzing the smooth or symplectic topology of \(M_G\) as well as the embedding of \(D\) in \(M_G\). In this paper, an investigation on the symplectic Kodaira dimension \(\kappa^s\) of \(M_G\) is initiated. In particular, we conjecture that \(\kappa^s(M_G)\leq \kappa^s(M)\). The inequality is verified for several classes of symplectic \(G\)-actions, including any actions on a rational surface or a symplectic 4-manifold with \(\kappa^s=0\).