The Dyer-Lashof algebra and the Steenrod algebra for generalized homology and cohomology

An analogue R of the Dyer-Lashof algebra R and an analogue A of the Steenrod algebra A are defined for generalized homology and cohomology theories. It is shown that if there is an E∞-multiplicative structure on a spectrum H, then on the corresponding generalized cohomology H*(X) of a topological space X there is an action AxH*(X)→H*(X) of the Steenrod algebra, while if the space X is an E∞-space, then on the generalized homology H*(X) there is an action RxH*(X)→H*(X) of the Dyer-Lashof algebra. These actions are computed for cobordism of topological spaces. A connection is established between the Steenrod operations and the Landweber-Novikov operations