  We introduce a new generation of PARSEC-COLIBRI stellar isochrones that
include a detailed treatment of the thermally-pulsing asymptotic giant branch
(TP-AGB) phase, and covering a wide range of initial metallicities
(0.0001<Zi<0.06). Compared to previous releases, the main novelties and
improvements are: use of new TP-AGB tracks and related atmosphere models and
spectra for M and C-type stars; inclusion of the surface H+He+CNO abundances in
the isochrone tables, accounting for the effects of diffusion, dredge-up
episodes and hot-bottom burning; inclusion of complete thermal pulse cycles,
with a complete description of the in-cycle changes in the stellar parameters;
new pulsation models to describe the long-period variability in the fundamental
and first overtone modes; new dust models that follow the growth of the grains
during the AGB evolution, in combination with radiative transfer calculations
for the reprocessing of the photospheric emission. Overall, these improvements
are expected to lead to a more consistent and detailed description of
properties of TP-AGB stars expected in resolved stellar populations, especially
in regard to their mean photometric properties from optical to mid-infrared
wavelengths. We illustrate the expected numbers of TP-AGB stars of different
types in stellar populations covering a wide range of ages and initial
metallicities, providing further details on the C-star island that appears at
intermediate values of age and metallicity, and about the AGB-boosting effect
that occurs at ages close to 1.6 Gyr for populations of all metallicities. The
isochrones are available through a new dedicated web server.
