We present a study of the evolution of brightest cluster galaxies (BCGs) in a sample of clusters at $0.05 \leq z<0.35$ from the SDSS and WISE with halo masses in the range $6 \times 10^{13}M_\odot$ (massive groups) - $10^{15.5}M_\odot$ (Coma-like clusters). We analyse optical and infrared colours and stellar masses of BCGs as a function of the mass of their host haloes. We find that BCGs are mostly red and quiescent galaxies and that a minority ($\sim 9$\%) of them are star-forming. We find that the optical $g-r$ colours are consistent with those of red sequence galaxies at the same redshifts; however, we detect the presence of a tail of blue and mostly star-forming BCGs preferentially located in low-mass clusters and groups. Although the blue tail is dominated by star-forming galaxies, we find that star-forming BCGs may also have red $g-r$ colours, indicating dust-enshrouded star formation. The fraction of star-forming BCGs increases with redshift and decreases with cluster mass and BCG stellar mass. We find that cool-core clusters host both star-forming and quiescent BCGs; however, non cool-core clusters are dominated by quiescent BCGs. Star formation appears thus as the result of processes that depend on stellar mass, cluster mass and cooling state of the intra-cluster medium. Our results suggest no significant stellar mass growth at $z<0.35$, supporting the notion that BCGs had accreted most of their mass by $z = 0.35$. Overall we find a low (1\%) AGN fraction detected at IR wavelengths.
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