  We establish motivic versions of the theorems of Lin and Gunawardena, thereby
confirming the motivic Segal conjecture for the algebraic group $\mu_\ell$ of
$\ell$-th roots of unity, where $\ell$ is any prime. To achieve this we develop
motivic Singer constructions associated to the symmetric group $S_\ell$ and to
$\mu_\ell$, and introduce a delayed limit Adams spectral sequence.
