  Let K be a field of characteristic 0 and A be a rigid tensor K-linear
category. Let M be a finite-dimensional object of A in the sense of
Kimura-O'Sullivan. We prove that the "motivic" zeta function of M with
coefficients in K\_0(A) has a functional equation. When A is the category of
Chow motives over a field, we thus recover and generalise previous work of
Franziska Heinloth, who considered the case where M is the motive of an abelian
variety. We also get a functional equation for the zeta function of any motive
modulo homological equivalence over a finite field. Our functional equation
involves the "determinant" of M, an invertible object of A: this is the main
difference with Heinoth's equation. In her case, the determinant turns out to
be 1.
