Deubiquitinates histone H2A, a specific tag for epigenetic transcriptional repression, thereby acting as a coactivator. Deubiquitination of histone H2A releaves the repression of di- and trimethylation of histone H3 at 'Lys-4', resulting in regulation of transcriptional initiation. Regulates gene expression via histone H2A deubiquitination. Also capable of removing NEDD8 from NEDD8 conjugates but has no effect on Sentrin-1 conjugates. Deubiquitinates BAZ2A/TIP5 leading to its stabilization (By similarity). Thiol-dependent hydrolysis of ester, thioester, amide, peptide and isopeptide bonds formed by the C-terminal Gly of ubiquitin (a 76-residue protein attached to proteins as an intracellular targeting signal). Interacts with BEND3 and BAZ2A/TIP5. Belongs to the peptidase C19 family. USP21 subfamily.