What is the B cell receptor made up of?

The B cell receptor is a membrane-bound protein complex found on the surface of B cells. The Y shaped protein complex, which is also known as B cell surface immunoglobulin, is made up of four chains - two heavy chains and two light chains, which comprise two antigen-binding sites. The light chains form the variable antigen-binding sites while the heavy chains form the constant binding site. The chains are joined by disulfide bonds. Light chains are classified as either lambda or kappa, while the heavy chains can be IgG, IgA, IgM, IgD, or IgE isotypes. 

Signaling proteins associated with the BCR lie beneath the membrane-bound antibodies. They are responsible for transmitting the signals that are generated when the antibodies bind to antigens.