  Let X be a symmetric space of noncompact type and \Gamma a lattice in the
isometry group of X. We study the distribution of orbits of \Gamma acting on
the symmetric space X and its geometric boundary X(\infty). More precisely, for
any y in X and b in X(\infty), we investigate the distribution of the set
{(y\gamma,b\gamma^{-1}):\gamma\in\Gamma} in X\times X(\infty). It is proved, in
particular, that the orbits of \Gamma in the Furstenberg boundary are
equidistributed, and that the orbits of \Gamma in X are equidistributed in
``sectors'' defined with respect to a Cartan decomposition. We also discuss an
application to the Patterson-Sullivan theory. Our main tools are the strong
wavefront lemma and the equidistribution of solvable flows on homogeneous
spaces.
