  We investigate the chemical and kinematic properties of the diffuse stellar
haloes of six simulated Milky Way-like galaxies from the Aquarius Project.
Binding energy criteria are adopted to defined two dynamically distinct stellar
populations: the diffuse inner and outer haloes, which comprise different
stellar sub-populations with particular chemical and kinematic characteristics.
Our simulated inner- and outer-halo stellar populations have received
contributions from debris stars (formed in sub-galactic systems while they were
outside the virial radius of the main progenitor galaxies) and endo-debris
stars (those formed in gas-rich sub-galactic systems inside the dark matter
haloes). The inner haloes possess an additional contribution from disc-heated
stars in the range $\sim 3 - 30 %$, with a mean of $\sim 20% $. Disc-heated
stars might exhibit signatures of kinematical support, in particular among the
youngest ones. Endo-debris plus disc-heated stars define the so-called \insitu
stellar populations. In both the inner- and outer-halo stellar populations, we
detect contributions from stars with moderate to low [$\alpha$/Fe] ratios,
mainly associated with the endo-debris or disc-heated sub-populations. The
observed abundance gradients in the inner-halo regions are influenced by both
the level of chemical enrichment and the relative contributions from each
stellar sub-population. Steeper abundance gradients in the inner-halo regions
are related to contributions from the disc-heated and endo-debris stars, which
tend to be found at lower binding energies than debris stars. (Abridged).
