Existence of characters for the discrete series.- Existence of characters in the general case.- Supercusp forms and supercuspidal representations.- The space A(G, ?).- The behavior of the characters of the supercuspidal representations on the regular set.- The mapping "Ff" (char ?=0).- The local summability of (char ?=0).- The local summability of the characters of the supercuspidal representations (char ?=0).