Feign

verb

1. To make a false show or pretence of; to counterfeit or simulate.

   "The pupil feigned sickness on the day of his exam."

2. To imagine; to invent; to pretend.

   "He feigned that he had gone home at the appointed time."

3. To make an action as if doing one thing, but actually doing another, for example to trick an opponent.
4. To hide or conceal.

   "Jessica feigned the fact that she had not done her homework."