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Let G be a semisimple group over rational numbers and H is a subgroup overrational numbers. Given a representation of G and an integral vector x whosestabilizer is equal to H. In this paper we investigate the asymptotic ofintegral points on Gx with bounded height. We find its asymptotic up to animplicit constant when H is large in G but we allow the presence ofintermediate subgroups. This is achieved by a novel combination of twoequidistribution results in two different settings: one is that of Eskin, Mozesand Shah on a Lie group modulo a lattice and the other one is a result ofChamber-Loir and Tschinkel on a smooth projective variety with a normalcrossing divisor.

Counting integral points on some homogeneous varieties with large reductive stabilizers