Felgaer was twice Panamerican Junior Champion, in 2000 and 2001. He was awarded the title of Grandmaster (GM) in 2002.
He was Argentine Champion in 2001, 2007, 2008, 2010, and 2014.
In 2001, he shared first at Mar del Plata and took 7th in Buenos Aires (14th Najdorf Memorial; Anatoly Karpov won). In 2003, he tied for 2nd-9th in Lido degli Estensi (Artur Kogan won). In 2004, he tied for 3rd-5th in Havana (Capablanca Memorial; Leinier Domínguez won).
In 2005, Felgaer won in Vila de Sort, tied for 2nd-5th at Sevilla 2005 (Dos Hermanas, Teimour Radjabov won), and took 6th at Barcelona 2005 (Vassily Ivanchuk won). In October 2006 he played in a match Buenos Aires vs Warsaw, and drew with Bartosz Soćko (1 : 1) at first board in Buenos Aires (17th Najdorf Festival).
Felgaer played for Argentina in three Chess Olympiads.
He participated in the FIDE World Chess Championship 2002 (knocked out in the first round by Loek van Wely) and in the FIDE World Chess Championship 2004 (knocked out in the second round by Alexey Dreev).