  We give a tool for understanding simplicial desuspension in A1-algebraic
topology: we show that $X \to \Omega (S^1 \wedge X)\to \Omega (S^1 \wedge X
\wedge X)$ is a fiber sequence up to homotopy in 2-localized A1-algebraic
topology for $X = (S^1)^m \wedge G_m^{\wedge q}$ with $m>1$. It follows that
there is an EHP sequence spectral sequence $$Z_{(2)} \otimes \pi_{n+1+i}^{A1}
(S^{2n+2m+1} \wedge (G_m)^{\wedge 2q}) \Rightarrow Z_{(2)} \otimes \pi_{i}^{A1,
s} (S^{m} \wedge (G_m)^{\wedge q}).$$
