When someone acts in a untrustworthy or underhanded way, they behave perfidiously. Your little brother might perfidiously insist that he was not the person who ate an entire package of Oreos.
People who lie or cheat act perfidiously, whether they're high school students stealing the answer key to a test or giant corporations using chemicals they claim are safe while knowing they may harm their customers. The adverb perfidiously comes from the adjective perfidious, or "deceitful." The root is Latin: perfidiosus, or "treacherous" is from perfidia, "faithlessness or falsehood," from the root phrase per fidem decipere, "to deceive through trustingness."