Spherical functions and character sheaves, according to A. Henderson.

Let $G$ be a connected reductive algebraic group defined over $\Bbb{F}_q$, and let $F$ be its Frobenius endomorphism. Let $\theta:G\rightarrow G$ be an algebraic group involution which commutes with $F$.A. Henderson has applied to the study of the spherical functions (average of the irreducible characters) of the symmetric space $G^F/(G^\theta)^F$ the theory of character sheaves introduced by G. Lusztig to study the characters of $G^F$,

The purpose of this talk is to explain A. Henderson's method in the general case and then to consider more particularly the case of the symmetric space $GL_n(\Bbb{F}_{q^2})/GL_n(\Bbb{F}_q)$ where the spherical functions are determined.