  Given an infinite reductive group G acting on an affine scheme X over C and a
Hilbert function h: Irr G \to N_0, we construct the moduli space M_{\theta}(X)
of \theta-stable (G,h)-constellations on X, which is a generalization of the
invariant Hilbert scheme after Alexeev and Brion and an analogue of the moduli
space of \theta-stable G-constellations for finite groups introduced by Craw
and Ishii. Our construction of a morphism M_{\theta}(X) \to X//G makes this
moduli space a candidate for a resolution of singularities of the quotient
X//G.
