General words:
* Feigning
* Pretending
* Affecting
* Playing dumb
* Shamming
More specific words:
* Obfuscating (intentionally making something unclear)
* Dissembling (deceptively concealing the truth)
* Evading (avoiding answering directly)
* Dodging (skillfully avoiding a difficult question)
* Malingering (pretending to be ill or injured to avoid work)
* Pleading ignorance (claiming to not know something even though you do)
The best word to use will depend on the specific context. For example, "playing dumb" might be a more casual term, while "dissembling" would be more formal and suggest a more deliberate attempt to deceive.