For a more formal way to say pretend to or imitate, choose the verb feign. You might feign indifference when you hear about some gossip, but you're probably dying to know.
Feign comes from the Latin fingere "to devise, fabricate." The word fiction comes from the same source, so if you feign something such as sleep, you give off the fiction that you are sleeping. This can be done to be polite but also to deceive such as when you feign an injury or the flu so you can stay home from school or work. You can also feign an accent, though some are better at this than others.