  We prove that, over a perfect field, Bredon motivic cohomology can be
computed by Suslin-Friedlander complexes of equivariant equidimensional cycles.
Partly based on this result we completely identify Bredon motivic cohomology of
a quadratically closed field and of a euclidian field in weights 1 and
$\sigma$. We also prove that Bredon motivic cohomology of an arbitrary field in
weight 0 with integer coefficients coincides (as abstract groups) with Bredon
cohomology of a point.
