  This paper consists of two main results. In the first one we describe all
Kaehler immersions of a bounded symmetric domain into the infinite dimensional
complex projective space in terms of the Wallach set of the domain. In the
second one we exhibit an example of complete and non-homogeneous
Kaehler-Einstein metric with negative scalar curvature which admits a Kaehler
immersion into the infinite dimensional complex projective space.
