Receptor for class I MHC antigens. Recognizes a broad spectrum of HLA-A, HLA-B, HLA-C, HLA-G and HLA-F alleles. Involved in the down-regulation of the immune response and the development of tolerance. Recognizes HLA-G in complex with B2M/beta-2 microglobulin and a nonamer self-peptide (peptide-bound HLA-G-B2M) triggering differentiation of type 1 regulatory T cells and myeloid-derived suppressor cells, both of which actively maintain maternal-fetal tolerance. Competes with CD8A for binding to class I MHC antigens. Inhibits FCGR1A-mediated phosphorylation of cellular proteins and mobilization of intracellular calcium ions.