I am looking for a reference/idea, how this passage from Labesse's Snowbird Lecture "Introduction to endoscopy" pg.5 can be explained:



> 
> "We shall denote by $f\_\pi$ a pseudo-coefficient for $\pi$, although it is highly non
>  unique. But as regards invariant harmonic analysis this plays no role. In
>  particular the orbital integrals are independent of the choice of the pseudocoefficient;
>  they are also independent of the choice of the Haar measure on
>  $G(F)$ but one has to use the canonical measure on the compact torus $G
> (F)$.
>  The orbital integrals of $f\_\pi$ are easily computed for 
>  regular semisimple:
>  $$O\_\gamma(f\_\pi) =\begin{cases} \Theta\_\pi(\gamma), & \gamma \mathrm{ elliptic}, \newline 0, &\mathrm{else},\end{cases} $$
>  where $\Theta\_\pi(\gamma)$ is the character of $\pi$."
> 
> 
> 


Here $G$ is a reductive group over a local field $F$ and $\pi$ a squareintegrable representation.



Pseudo coefficients and orbital integrals
Existence of pseudo-coefficients for square-integrable representations (and the link with character values of the representations) is stated and proved in 


D. Kazhdan, Cuspidal geometry of $p$-adic groups.
J. Analyse Math. 47 (1986), 1–36. 


