  The aim of this paper is to define an n-1-cocycle $\sigma$ on $\GL_{n}(\Q)$
with values in a certain space $\hD$ of distributions on
$\A_f^{n}\setminus\{0\}$. Here $\A_f$ denotes the ring of finite ad\`{e}les of
$\Q$, and the distributions take values in the Laurent series
$\C((z_{1},...,z_{n}))$. This cocycle can be used to evaluate special values of
Artin L-functions on number fields at negative integers. The construction
generalizes that of Solomon in the case n=2.
