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.