Catalyzes the formation of 5-oxoproline from gamma-glutamyl dipeptides and may play a significant role in glutathione homeostasis (PubMed:18515354). Induces release of cytochrome c from mitochondria with resultant induction of apoptosis (PubMed:16765912). an alpha-(gamma-L-glutamyl)-L-amino acid = 5-oxo-L-proline + an L-alpha-amino acid Homodimer. By geranylgeraniol. Belongs to the gamma-glutamylcyclotransferase family.