Abstract: We introduce crossed interval groups and construct a crossed interval analog IS of the Fiedorowicz-Loday symmetric category. We prove that the functor F(-) of the free IS-extension of an I-object does not change homotopy type. We then observe that the operad B of natural operations on the Hochschild cohomology equals F(T), where T is an operad whose homotopy type is known. We conclude from these facts that B has the homotopy type of the operad of singular chains on the little disks operad.