Kleiman’s criterion states that, for X a projective scheme, a divisor D is ample if and only if it pairs positively with every non-zero element of the closure of the cone of curves. In other words, the cone of ample divisors in \(N^1(X)\) is the interior of the nef cone. In this paper we present an analogous statement for a variety X acted on by a reductive group G with a choice of G-linearization \(L \to X\) . In this new context, the ample cone of X is replaced by a cell in the variation of GIT decomposition of the G-ample cone, and curves in X are replaced by quasimaps to \([X/G]\) .