  The aim of this paper is to show that the most elementary homotopy theory of
$\mathbf{G}$-spaces is equivalent to a homotopy theory of simplicial sets over
$\mathbf{BG}$, where $\mathbf{G}$ is a fixed group. Both homotopy theories are
presented as Relative categories. We establish the equivalence by constructing
a strict homotopy equivalence between the two relative categories. No Model
category structure is assumed on either Relative Category.
