Is there someone who knows the title of the original publication of Grothendieck on the construction of the Grothendieck group?
Thanks in advance.
What seems to be clear is that the origin of the Grothendieck group is Grothendieck's work on Riemann-Roch's theorem around 1956.
According to Weibel's The Development of Algebraic K-theory before 1980 (which is certainly worth reading!), the original source is Classes de faisceaux et théorème de Riemann-Roch, some mimeographed notes from 1957 who were later published (in 1971) in Théorie des intersections et théorème de Riemann-Roch (SGA6).
In his Lecture Notes on Algebraic K-theory, Rognes links to Borel and Serre, Le théorème de Riemann-Roch, Bulletin de la Société Mathématique de France 86 (1958) “for the published exposition.”