An ethnic group, or an ethnicity, is a category of people who identify with each other based on similarities such as common ancestry, language, society, culture or nation
I would dispute the notion of common ancestry is synonymous with common transfer of genes. The former is about descent, within a system of kinship, that may or may not recognize within it's domain an actual realized transfer of genes on the one hand, and may include in it's domain instances when no such transfer might have occurred (adoption/cuckoldry/politically motivated claims of kinship/etc.etc.).
come on, you are engaging in pointless sophistry. Common ancestry doesn't mean that it involves 100% guaranteed common transfer of genes every time - it just means that common transfer of genes was quite likely to take place at least relatively often. In the case of Ashkenazi Jews, we know it did.