Steenrod operations in SHC-algebras

In this paper we use Mayʹs algebraic approach to Steenrod operation in conjunction with Munkholmʹs notion of shc-algebra in order to introduce what we call a π-shc-algebra. (π is a cyclic group of order a fixed prime p.) We prove that the homology and the Hochschild homology of a π-shc-algebra have natural Steenrod operations. Our main topological example is the free loop space. We prove that the Jones’ isomorphism preserves Steenrod operations.