Cellular operads and iterated loop spaces

The configuration space of p-tuples of pairwise distinct points in R(infinity) carries a natural filtration coming from the inclusions of the R(n) into R(infinity). We characterize the homotopy type of this filtration by the combinatorial properties of an underlying cellular structure and establish a close relationship to May's theory of E(n)-operads. This gives a unified approach to the different known combinatorial models of iterated loop spaces reproving by the way the approximation theorems of Mile;ram, Smith and Kashiwabara.