  The endomorphism ring of the projective plane over a field F of
characteristic neither two nor three is slightly more complicated in the
Morel-Voevodsky motivic stable homotopy category than in Voevodsky's derived
category of motives. In particular, it is not commutative precisely if there
exists a square in F which does not admit a sixth root. A byproduct of the
computations is a proof of Suslin's conjecture on the Suslin-Hurewicz
homomorphism from Quillen to Milnor K-theory in degree four, based on work of
Asok, Fasel, and Williams.
