  Symmetric $k$-varieties are a natural generalization of symmetric spaces to
general fields $k$. We study the action of minimal parabolic $k$-subgroups on
symmetric $k$-varieties and define a map that embeds these orbits within the
orbits corresponding to algebraically closed fields. We develop a condition for
the surjectivity of this map in the case of $k$-split groups that depends only
on the dimension of a maximal $k$-split torus contained within the fixed point
group of the involution defining the symmetric $k$-variety.
