Adams operations ψk on K theory (algebraic or topological) are characterized by the following properties.
The fundamental idea is that for a vector bundle V on a topological space X, there is an analogy between Adams operators and exterior powers, in which as of the roots α of a polynomial P(t).
This calculation can be defined in a K-group, in which vector bundles may be formally combined by addition, subtraction and multiplication (tensor product).
In this special case the result of any Adams operation is naturally a vector bundle, not a linear combination of ones in K-theory.
Treating the line bundle direct factors formally as roots is something rather standard in algebraic topology (cf.