  Over a perfect field k, let G be an extension of an abelian variety by the
multiplicative group $\G_m$. We compute the motive of G in Voevodsky's category
of etale motivic complexes with rational coefficients. The result is a
decomposition similar to the classical decomposition of the Chow motive of an
abelian variety obtained by Deninger/Murre, Kuennemann, Shermenev and Scholl,
and other authors.
