For groups of prime order, equivariant stable maps between equivariant representation spheres are investigated using the Borel co\-ho\-mo\-logy Adams spectral sequence. Features of the equivariant stable homotopy category, such as stability and duality, are shown to lift to the category of modules over the associated Steenrod algebra. The dependence on the dimension functions of the representations is clarified.
Journal of Homotopy and Related Structures, Vol. 2(2007), No. 1, pp. 141-162