Towards the dual motivic Steenrod algebra in positive characteristic

The dual motivic Steenrod algebra with mod $ell$ coefficients was computed by Voevodsky over a base field of characteristic zero, and by Hoyois, Kelly, and {O}stv{ae}r over a base field of characteristic $p eq ell$. In the case $p = ell$, we show that the conjectured answer is a retract of the actual answer. We also describe the slices of the algebraic cobordism spectrum $MGL$: we show that the conjectured form of $s_n MGL$ is a retract of the actual answer.