2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102135We study equivariant embeddings with small boundary of a given homogeneous space $G/H$, where $G$ is a connected, linear algebraic group with trivial Picard group and only trivial characters, and $H \subset G$ is an extension of a connected Grosshans subgroup by a torus. Under certain maximality conditions, like completeness, we obtain finiteness of the number of isomorphism classes of such embeddings, and we provide a combinatorial description the embbeddings and their morphisms. The latter allows a systematic treatment of examples and basic statements on the geometry of the equivariant embeddings of a given homogeneous space $G/H$.minor changes, 30 pages, to appear in J. AlgebraAlgebraic Geometry14L24, 14M17, 14M25text