Title: Symmetric cohomology of groups as a Mackey functor Authors: C.C. Todea; Abstract: Symmetric cohomology of groups, defined by M. Staic in \cite{St3D}, is similar to the way one defines the cyclic cohomology for algebras. We show that there is a well-defined restriction, conjugation and transfer map in symmetric cohomology, which form a Mackey functor under a restriction. Some new properties for the symmetric cohomology group using normalized cochains are also given Status: accepted/2014.