Is it permissible to perform a hair transplant operation in which hair is taken from the same person and placed in another area that is hairless?

It is permissible, according to Sharia (definition), to implant hair on the head. This is not considered the forbidden "joining" (wasl) and is not a change to Allah's creation. Rather, it is a restoration of what Allah created and falls under the category of permissible medical treatment, analogous to the story of the Companion who acquired a nose made of gold.