  In the Solar System, minor bodies and dust deliver various materials to
planetary surfaces. Several exoplanetary systems are known to host inner and
outer belts, analogues of the main asteroid belt and the Kuiper belt. We study
the possibility that exominor bodies and exodust deliver volatiles and
refractories to the exoplanets in the system HR8799 by performing N-body
simulations. The model consists of the host star, four giant planets (HR8799 e,
d, c, and b), 650000 test particles representing the inner belt, and 1450000
test particles representing the outer belt. Moreover we modelled dust
populations that originate from both belts. Within a million years, the two
belts evolve towards the expected dynamical structure (also derived in other
works), where mean-motion resonances with the planets carve the analogues of
Kirkwood gaps. We find that, after this point, the planets suffer impacts by
objects from the inner and outer belt at rates that are essentially constant
with time, while dust populations do not contribute significantly to the
delivery process. We convert the impact rates to volatile and refractory
delivery rates using our best estimates of the total mass contained in the
belts and their volatile and refractory content. Over their lifetime, the four
giant planets receive between $10^{-4}$ and $10^{-3}M_\bigoplus$ of material
from both belts. The total amount of delivered volatiles and refractories,
${5\times10^{-3}\textrm{M}_\bigoplus}$, is small compared to the total mass of
the planets, $11\times10^{3}\textrm{M}_\bigoplus$. However, if the planets were
formed to be volatile-rich, their exogenous enrichment in refractory material
may well be significant and observable, for example with JWST-MIRI. If
terrestrial planets exist within the snow line of the system, volatile delivery
would be an important astrobiological mechanism and may be observable as
atmospheric trace gases.
