  We discuss some results and conjectures related to the existence of the
non-nilpotent motivic maps $\eta$ and $\mu_9$. To this purpose, we establish a
theory of power operations for motivic $H_{\infty}$-spectra. Using this, we
show that the naive motivic analogue of the unstable Kahn-Priddy theorem fails.
Over the complex numbers, we show that the motivic $T$-spectrum
$S[\eta^{-1},\mu_9^{-1}]$ is closely related to higher Witt groups, where $S$
is the motivic sphere spectrum and $\eta$, $\sigma$ and $\mu_9$ are explicit
elements in $\pi_{**}(S)$.
