  Let K be an algebraically closed field of characteristic zero, G_m=(K\{0},*)
be its multiplicative group, and G_a=(K,+) be its additive group. Consider a
commutative linear algebraic group G=G_m^r\times G_a. We study equivariant
G-embeddings, i.e. normal G-varieties X containing G as an open orbit. We prove
that X is a toric variety and all such actions of G on X correspond to Demazure
roots of the fan of X. In these terms, the orbit structure of a G-variety X is
described.
