Compactifications of based-free G-spaces

For a compact Lie group G we characterize those based-free G-spaces which admit based-free G-compactifications. For such G-spaces a universal based-free compact G-space of a given infinite weight is constructed. Besides, we show that the maximal G-compactification βGX is based-free whenever X is a finitistic (in particular, finite-dimensional and paracompact) based-free G-space. We also give new charaterizations of βGX for such G-spaces.