In this case, I think that the site should look exactly the same for every alias. For example Facebook dot com won't be recognizable in India, Russia, or China because it's a different alphabet system. I'm thinking to have different .coms for the exact same site and each .com might be auto translated into that language.

Instead of translating using subdomains because with subdomains, the main domain would still be in Latin characters, but not in the characters of the person's native language.