  Let G be a semisimple complex algebraic group, and H a wonderful subgroup of
G. We prove several results relating the subgroup H to the properties of a
combinatorial invariant S of G/H, called its spherical system. It is also
possible to consider a spherical system S as a datum defined by purely
combinatorial axioms, and under certain circumstances our results prove the
existence of a wonderful subgroup H associated to S. As a byproduct, we reduce
for any group G the proof of the classification of wonderful G-varieties, known
as the Luna conjecture, to its verification on a small family of cases, called
primitive.
