  In this paper, we construct stable distributions on the set of elliptic
elements of an odd orthogonal groups (over a p-adic field with p large). Theses
distributions are of zero level. They are parametrised by Langlands like
parameters. In the second part of the paper, we show how to interpret these
distributions in term of characters of discrete series; this is conditional to
a result of A.-M. Aubert which announces how to reduce the zero level case to
the case of unipotent reduction using the Lusztig's induction. But, modulo this
explicit hypothesis, we prove that our computation will determine all the
stable linear combinations of discrete series of zero level for $SO(2n+1)$. The
link between the parameters of stable distributions and stable linear
combinations of discrete series is done by using a Fourier like involution on
the set of parameters.
