I have just started GMing a homebrew campaign with a group of relatively inexperienced players. I have only played with one of them before (I have GMed for him as well as been a fellow player with him), and he is notorious for being a problem player. In fact, I know of at least one group who refuses to play with him anymore.
Problems in the past have included dice fudging, not taking full amounts of damage in combat, stealing the spotlight from other players, and a number of other annoying things. All that said, I have known this guy for a while and consider him a friend.
The setting I am running is a generic fantasy world, loosely based on the Forgotten Realms, using the same gods and lore. I typically allow my players to take part in the world-building process, so they feel like their characters belong. However, this problem player is obsessed with Celtic and Viking mythology and has been attempting to insert them into the world, even giving his half-elf barbarian a very long and hard-to-pronounce Gaelic name and saying that he is from a place called "Ironland".
During session zero, I tried politely explaining that there are no Celts in this world, and suggested saving these ideas for a future game. This resulted in him pouting in the corner for 20 minutes.
How can I deal with this player trying to insert real-world mythology into a game? Am I being too overprotective of the world I am creating? Should I just allow him to create his own corner of the world?