  Exterior power operations provide an additional structure on K-groups of
schemes which lies at the heart of Grothendieck's Riemann-Roch theory. Over the
past decades, various authors have constructed such operations on higher
K-theory. In this paper, we prove that these constructions actually yield the
same operations. This leads to the proof of a conjecture by the first author
about composition of these operations in the equivariant context. As a
by-product we make the proof of Grayson's explicit description of higher
K-groups accessible to the reader not familiar with the language of spectra.
