Tuhia he tomokanga mō tēnei wāhanga - Mai i te tau 2000 ki te 2008, i whakataetae a Stefán i ngā whakataetae ā-ao e iwa mō Iceland: e rima ngā wā i te Chess Olympiad (2000)
, 2nd reserve board; 2002, reserve board; 2004, 2nd reserve board; 2006, reserve board; 2008, board 4) me nga wa e wha i te European Team Chess Championship (2001, te papa 4; 2003, te papa 3; 2005, te papa 2; 2007, te papa 4). Ko tana kaute katoa i te Olympiad he 23/41 (+ 18 <unk> 13 = 10), a ko tana kaute katoa i te Whakataetae Rōpū o Europi he 161⁄2/32 (+ 11 <unk> 10 = 11). Ko te hua pai o te Orimipia o Iceland me Stefán i runga i te kapa ko te 22 i te 2002, a ko to raatau hua pai o te whakataetae kapa Pakeha ko te 20 i te 2001 me te 2007.