  Using the global Kuranishi charts constructed in \cite{HS22}, we define
gravitational descendants and equivariant Gromov-Witten invariants for general
symplectic manifolds. We prove that that these invariants, equivariant and
non-equivariant, satisfy the axioms of Kontsevich and Manin and their
generalisations. A virtual localisation formula holds in this setting; we use
it derive an explicit formula for the equivariant GW invariants of a class of
Hamiltonian manifolds. A comparison with the GW invariants of \cite{RT97} is
given in the semipositive case.
