The Mummy Costume is a costume Sly can obtain in the episode Rob Like an Egyptian in Sly Cooper: Age of Thieves.
As the name implies, Sly takes on the appearance of a mummy. The wrappings are a light gray, covering everything from the tail to Sly's head, but keeping the eyes exposed so as to make sure that Sly can see. Sly also has a pharaoh's crook for pickpocketing.
"Made as a last ditch effort to avoid getting sunburns in the hot desert, Sly had managed to get some protection from the heat with wrappings meant for an actual mummy. With this costume, Sly can not only do what he normally can while not wearing the costume, but he can also wrap up guards, blinding them so that Sly can escape if he is ever seen. He can also access the fabled hidden locations that the many hidden sarcophagi are blocking. It may even lead him to treasure..."
While Sly can do his normal moves while in this costume, he isn't able to paraglide. However, by pressing the triangle button, Sly can wrap guards up in mummy wrappings. This will only work if only one guard has seen him, though. If Sly approaches a sarcophagus, it will open automatically, teleporting Sly to hidden locations only accessible via that particular sarcophagus.