0. The following is an outline of a theory of 11-projective RG-modules, where R is a ring, G a finite group and !1 a family of subgroups of G. The first section contains the obvious generalisations of Higman's theory of relatively U-projective RG-modules and Green's theory of vertices, e.g. (1) any RGmodule is 11-projective with 11= {@IP R # R } (p a prime, Gp a p-Sylow-subgroup), (2) for any M there exists a family of vertices 11(M), such that M is ~B-projective if and only if any subgroup in 11(M) is contained in a conjugate of a subgroup in !'][B (11(M) and ~13 families of subgroups of G). In the second section we study a certain ideal P(M, 11) in R, which is defined for any RG-module M and family of subgroups 11 and measures to some extent the U-projectivity of M, i.e. P(M, 11)= R r is 11-projective. In the third section we compute P(M, 11) for various M and 1I. We get especially: an ideal 9.I_~R is of the form P(M, 11) for some M if and only if (G: U)eg.I for all Ue11. In Sections 4 and 5 we study the behavior of lI-projectivity under ring extensions. If R is noetherian and R~ the 931-adic completion (gJ~ a maximal ideal in R) then M is 11-projective if and only i f / ~ | M is 11-projective for all 9J/with ]G]Eg~. If M is projective as R-module and ]GI not a zero divisor in R, then P(M, 11) = P(M/] G[. M, 11), especially M is 11-projective if and only ifM/IG]. M is. This relates our theory to the cases considered by Higman and Green. In the last section we give a generalisation of a result due to Jones, concerning the finiteness of the number of nonisomorphic indecomposable 11projective RG-modules and mention a few more results, which will be worked out in another connection.