Let $\pi$ be an irreducible cuspidal representation of a semi-simple $p$-adic group $G$. It is well-known that the character of $\pi$ is concentrated in the set of compact elements in $G$.


What is the best reference for this result?
Also, if there is a really simple proof of this result, I would be glad to learn it!



Characters of cuspidal representations
This is an old result due to Deligne:


Le support du caractère d'une représentation supercuspidale. 
C. R. Acad. Sci. Paris Sér. A-B 283 (1976), no. 4, Aii, A155–A157. 


