Henrik Ibsen's play "Peer Gynt" digs deep into the question of what it means to be oneself. An upcoming computer game version invites players to take on the role of Peer and thereby raises new questions about identity and identification. By recording dyads of students who play an early version of the game and analysing their interaction during gameplay, we examine how students collaboratively make meaning of the computer game. This study employs a sociocultural and dialogic approach to meaning making. In the analysis, we draw on Gee's theory on multiple player identities and see the dyads playing together as two "real-world" selves negotiating on creating one "virtual" self through a co-authorship of situated meaning in what Gee calls the "projective stance." To better understand their cooperation in this undertaking, we also apply Goffman's term "activity frames." The analysis shows how the dyads approach the game in different ways by establishing frames in which they interpret, impersonate or recreate Peer, in order to make meaning of their gameplay.