  We consider the K-theory of the Hilbert scheme of points in the complex
plane, which under McKay correspondence is isomorphic to the space of symmetric
functions $\Lambda^n$. We prove a formula conjectured by Boissi\`ere for the
endomorphism of $\Lambda^n$ induced by multiplication by the classes of the
Adams powers of the tautological bundle. We describe the structure constants
for the multiplication on $\Lambda^n$ induced by the tensor product in
K-theory.
