Higher algebraic K-theory carries the structure of a lambda-ring,
which determines Adams operations, the gamma filtration and other
useful tools for analysing K-theory. The higher K-groups and
lambda-operations are usually defined with homotopy theory, and
as such are often difficult to work with explicitly. Recently Grayson
has given an entirely algebraic construction of the higher algebraic
K-groups. In this talk I will describe Grayson's construction, and
explain how it can be used to give a new construction of the lambda-ring
structure on the higher K-groups of a scheme. This is joint work with
Bernhard Koeck and Lenny Taelman.