  We generalize the notion of a projective profinite group to a projective pair
of a profinite group and a closed subgroup. We establish the connection with
Pseudo Algebraically Closed (PAC) extensions of PAC fields: Let M be an
algebraic extension of a PAC field K. Then M/K is PAC if and only if the
corresponding pair of absolute Galois groups (Gal(M),Gal(K)) is projective.
Moreover any projective pair can be realized as absolute Galois groups of a PAC
extension of a PAC field.
  Using this characterization we construct new examples of PAC extensions of
relatively small fields, e.g., unbounded abelian extensions of the rational
numbers.
