Tezcatlipoca

Tezcatlipoca (テスカトリポカ) is a Magic God of Aztec Mythology and a member of the true Gremlin, first mentioned in Shinyaku Toaru Majutsu no Index Volume 13.

Etymology
(often translated as 'Smoking Mirror' from Nahuatl) is a major god in Aztec Mythology, associated with obsidian, the night, jaguars, sorcery and strife, among other things. He is said to have cooperated with Quetzalcoatl to create the world from the body of the monster Cipactli, losing his foot in the process. He is also said to have acted as the First Sun but was knocked from the sky by Quetzalcoatl and destroyed the world in anger, in the form of a jaguar. He also caused the ends of the three following worlds before the current world and the Fifth Sun.

Magic God Invasion Arc
At some point around the time of the incident instigated by the High Priest, Tezcatlipoca encountered Kamisato Kakeru and was 'exiled' by his World Rejecter.