  Let F be a finite extension of Q_p and let G be a connected reductive group
over F. We assume that p is big relatively to G. Let G' be an endoscopic group
of G. Following Arthur, we have, roughly speaking, a spectral transfer which,
to a stable finite linear combination of irreducible admissible representations
of G'(F), associates a finite linear combination of irreducible admissible
representations of G(F). Let p^{0,G} be the Bernstein's projector such that,
for an irreducible admissible representation $\pi$ of G(F), we have
p^{0,G}($\pi$)=$\pi$ if $\pi$ has level 0 and p^{0,G}($\pi$)=0 if $\pi$ has
strictly positive level. Define similarly p^{0,G'}. We prove that p^{0,G'}
preserves the space of stable finite linear combination of irreducible
admissible representations of G'(F) and that p^{0,G} transfer=transfer
p^{0,G'}.
