We discuss some results and conjectures related to the existence of the non-nilpotent motivic maps
η
\eta
and
μ
9
\mu _9
. To this purpose, we establish a theory of power operations for motivic
H
∞
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
T
-spectrum
S
[
η
−
1
,
μ
9
−
1
]
S[\eta ^{-1},\mu _9^{-1}]
is closely related to higher Witt groups, where
S
S
is the motivic sphere spectrum and
η
\eta
and
μ
9
\mu _9
are explicit elements in
π
∗
∗
(
S
)
\pi _{**}(S)
.