A.D. Elmendorf and J.P. May, Algebras over equivariant sphere spectra Abstract. We study algebras over the sphere spectrum S_G of a compact Lie group G. In particular, we show how to construct S_G-algebras from S-algebras, where S is the nonequivariant sphere spectrum. This gives a reservoir of equivariant examples to which recently developed algebraic techniques in stable homotopy theory can be applied. A special case will be used in a companion paper of Benson and Greenlees to study the ordinary cohomology of the classifying space BG.