  A \emph{multicontraction} on a Hilbert space $\HH$ is an $n$-tuple of
operators $T=(T_1,...,T_n)$ acting on $\HH$, such that $\sum_{i=1}^n T_i
T_i^*\le \1_\HH$. We obtain some results related to the characteristic function
of a commuting multicontraction, most notably discussing its behaviour with
respect to the action of the analytic automorphisms of the unit ball.
