Take the tour ×  Status: Questions 2 and 4 answered in the
negative. Questions 1 and 3 ARE STILL UNANSWERED, despite
previous claims.  On the third page of Wolfang K. Seiler's paper
"lambda-rings and Adams operations in algebraic K-Theory" (pp.
93-102 in Beilinson's Conjectures), it is claimed that the
Grothendieck ring of representations of a given group $G$ over a
given commutative ring $A$ modulo exact sequences is a special
$\lambda$-ring. Here, "representations" means finitely-generated
projective $A$-modules with a $G$-module structure. ("Special
$\lambda$-ring" is what most people just call "$\lambda$-ring",
as opposed to "pre-$\lambda$-ring".)  1. Does anybody know a
proof of this? I don't understand the sketched proof in 1, and I
don't have the reference (R. G. Swan, A splitting principle in
algebraic $K$-theory, in: Representation theory of finite groups
and related topics, Proc. Symp. Pure Math. 21 (1971), 155-159)
either. I have been told that Atiyah-Tall has a proof, but I am
very skeptical about