Virtual reality (VR) allows embodying any possible avatar. Known as the Proteus effect, avatars can change users’ behavior and attitudes. Previous work found that embodying Albert Einstein can increase cognitive task performance. The behavioral confirmation paradigm, however, predicts that our behavior is also affected by others’ perception of us. Therefore, we investigated the cognitive performance in collaborative VR when self-perception and external perception of the own avatar differ. 32 male participants performed a Tower of London task in pairs. One participant embodied Einstein or a young adult while the other perceived the participant as Einstein or a young adult. We show that the perception by others affects cognitive performance. The Einstein avatar also decreased the perceived workload. Results imply that avatars’ appearance to both, the user and the others must be considered when designing for cognitively demanding tasks.