  In this note, we consider a non-commutative analogy of the classical
Fefferman multiplier problem for the ball. More precisely, if $\chi$ is the
characteristic function of the unit interval $I=[0,1],$ we investigate a family
of differential operators $\mathcal{R}$ on a graded Lie group $G,$ for which
the multipliers $\chi(\mathcal{R})$ are bounded on $L^p(G),$ if and only if
$p=2.$
