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