Introductory and pedagogical treatmeant of the article : P. Broussous
"Distinction of the Steinberg representation", with an appendix by Fran\c{c}ois
Court\`es, IMRN 2014, no 11, 3140-3157. To appear in Proceedings of Chaire Jean
Morlet, Dipendra Prasad, Volker Heiermann Ed. 2017. Contains modified and
simplified proofs of loc. cit. This article is written in memory of
Fran\c{c}ois Court\`es who passed away in september 2016.Comment: 33 pages, 4 figure