On conjugation invariants in the dual Steenrod algebra

We investigate the canonical conjugation, chi, of the mod 2 dual Steenrod a lgebra, A(*), with a view to determining the subspace, A(*)(chi), of elemen ts invariant under chi. We give bounds on the dimension of this subspace fo r each degree and show that, after inverting xi(1), it becomes polynomial o n a natural set of generators. Finally we note that, without inverting xi(1 ), A(*)(chi) is far from being polynomial.