The aim of this paper is to apply algebro-geometric Szego kernels to the asymptotic study of a class of trace formulae in equivariant geometric quantization and algebraic geometry. Let (M,J) be a connected complex projective manifold, of complex dimension d, and let A be an ample line bundle on it. Let, in addition, G be a compact and connected g-dimensional Lie group acting holomorphically on M in such a way that the action can be linearized to A. For every k ∈ N, the spaces of global holomorphic sections H ( M,A ) are linear representations of G and therefore may be equivariantly decomposed over its irreducible representations. More precisely, let g be the Lie algebra of G, and let Λ ⊆ g be a set of weights parametrizing the family of all finite-dimensional irreducible representations of G. For every ∈ Λ, denote by V the corresponding G-module. Given ∈ Λ and a linear representation of G on a finite dimensional vector space W , we denote by W ⊆ W the -isotype of W , that is, the maximal invariant subspace of W equivariantly isomorphic to a direct sum of copies of V . For every k ∈ N, we then have equivariant direct sum decompositions