Let \(G\) be a finite group, and let \(\mathcal O\) be a suitable ring of coefficients. To every indecomposable \({\mathcal O} G\)-lattice \(M\), there are attached three invariants: (1) its vertex \(P\), a subgroup of \(G\), (2) its source \(L\), an indecomposable \({\mathcal O} P\)-lattice, (3) a multiplicity module \(W\), an indecomposable projective lattice over a twisted group algebra of the stabilizer of \(L\) in \(N_ G(P)\). The paper intends to make precise the statement that these triples \((P, L, W)\) parametrize the isomorphism classes of indecomposable \({\mathcal O} G\)-lattices. More generally, the author gives a parametrization of primitive interior \(G\)- algebras over \(\mathcal O\). \textit{L. Puig} has expressed a different point of view on some aspects of this paper. The interested reader may want to refer to [Math. Z. 215, 321-335 (1994; Zbl 0798.20006)] for details.