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In this paper we give detailed construction of $G$-equivariant Kuranishichart of moduli spaces of pseudo-holomorphic curves to a symplectic manifoldwith $G$-action, for an arbitrary compact Lie group $G$. The proof is based onthe deformation theory of {\it unstable} marked curves using the language ofLie groupoid (which is {\it not} necessary etale) and the Riemannnian center ofmass technique. This proof is actually similar to [FOn,Sections 13 and 15]except the usage of the language of Lie groupoid makes the argument moretransparent. This version correct some errors of the previous versionespecially those pointed out by the referee.

Lie groupoid, deformation of unstable curve, and construction of equivariant Kuranishi charts