While each character of a finite group determines the underlying matrix representation, up to change of basis, it is often very difficult to give the representation explicitly even when the character is completely explicit. We prove a general result which gives representations from characters. The motivation is a theorem of S.Gelfand which gives certain "cuspidal" representations of GL(n,q) in terms of so-called "Bessel functions". We show that Gelfand's result is much more general and can be proved in a wide context.