Context : We investigate the stellar population and the origin of diffuse light around brightest cluster galaxies .

Aims : We study the stellar population of the dynamically hot stellar halo of NGC 3311 , the brightest galaxy in the Hydra I cluster , and that of photometric substructures in the diffuse light to constrain the origin of these components .

Methods : We analyze absorption lines in medium-resolution , long-slit spectra in the wavelength range 4800 – 5800 Å obtained with FORS2 at the Very Large Telescope .
We measure the equivalent width of Lick indices out to 20 kpc from the center of NGC 3311 and fit them with stellar population models that account for the [ \alpha /Fe ] overabundance .

Results : Stars in the dynamically hot halo of NGC 3311 are old ( age > 13 Gyr ) , metal-poor ( [ Z/H ] \sim - 0.35 ) , and alpha-enhanced ( [ \alpha /Fe ] \sim 0.48 ) .
Together with the high velocity dispersion , these measurements indicate that the stars in the halo were accreted from the outskirts of other early-type galaxies , with a possible contribution from dwarf galaxies .
We identify a region in the halo of NGC 3311 associated with a photometric substructure where the stellar population is even more metal-poor ( [ Z/H ] \sim - 0.73 ) .
In this region , our measurements are consistent with a composite stellar population superposed along the line of sight , consisting of stars from the dynamically hot halo of NGC 3311 and stars stripped from dwarf galaxies .
The latter component contributes \leq 28 % to the local surface brightness .

Conclusions : The build-up of diffuse light around NGC 3311 is on-going .
Based on the observed stellar population properties , the dominant part of these stars may have come from the outskirts of bright early-type galaxies , while stars from stripped dwarf galaxies are presently being added .