  We use publicly available galaxy merger trees, obtained applying
semi-analytic techniques to a large high resolution cosmological simulation, to
study the environmental history of group and cluster galaxies. Our results
highlight the existence of an intrinsic history bias which makes the nature
versus nurture (as well as the mass versus environment) debate inherently ill
posed. In particular we show that: (i) surviving massive satellites were
accreted later than their less massive counterparts, from more massive haloes;
(ii) the mixing of galaxy populations is incomplete during halo assembly, which
creates a correlation between the time a galaxy becomes satellite and its
present distance from the parent halo centre. The weakest trends are found for
the most massive satellites, as a result of efficient dynamical friction and
late formation times of massive haloes. A large fraction of the most massive
group/cluster members are accreted onto the main progenitor of the final halo
as central galaxies, while about half of the galaxies with low and intermediate
stellar mass are accreted as satellites. Large fractions of group and cluster
galaxies (in particular those of low stellar mass) have therefore been
`pre-processed' as satellites of groups with mass ~10^13 Msun. To quantify the
relevance of hierarchical structure growth on the observed environmental
trends, we have considered observational estimates of the passive galaxy
fractions, and their variation as a function of halo mass and cluster-centric
distance. Comparisons with our theoretical predictions require relatively long
times (~5-7 Gyr) for the suppression of star formation in group and cluster
satellites. [abridged]
