Which of the following statements is false?

Class II proteins consist of two polypeptide chains, namely alpha and beta chains, and both chains exhibit significant polymorphism. This polymorphism is crucial for the diversity of the T-cell response, as it allows for a wide variety of peptide presentations to T cells. Therefore, the statement indicating that class II proteins have polymorphism in only one of the two polypeptide chains is incorrect, making it the false statement in this scenario.

In contrast, class I proteins do present polymorphism mainly in the alpha chain, which is vital for their role in antigen presentation to CD8+ T cells. Class III proteins, while varying in function, are indeed located on chromosome 6 alongside class I and class II genes, contributing to the broader immune response. The role of 2M (beta-2-microglobulin) is important in the context of class I molecules but is less critical in bone marrow transplantation compared to other factors like HLA matching, meaning the statement concerning its subtyping can be considered true.