Antigen-presenting protein that binds self and non-self glycolipids and presents them to T-cell receptors on natural killer T-cells. Heterodimer with B2M (beta-2-microglobulin). Interacts with MHC II and CD74 (By similarity). Subject to intracellular trafficking between the cell membrane, endosomes and lysosomes. During protein synthesis and maturation, CD1 family members bind endogenous lipids that are replaced by lipid or glycolipid antigens when the proteins are internalized and pass through endosomes, before trafficking back to the cell surface.