Pedzisa mutsara unotevera: González akaita mutambo wake wepasi rose wechikwata chenyika cheVenezuela musi wa 23 Ndira 1993, mukukwikwidza 0<unk>0 vachipesana nePeru. Akamirira nyika mumitambo mitatu yeCopa América (1993,
1995 uye 1997), uye akapedza makore gumi nerimwe asina kutamba kudivi kusvika pakupedzisira kwake muna 2008.