  We construct a combinatorially defined involution on the algebraic $K$-theory
of the ring spectrum associated to a bimonoidal category with anti-involution.
Particular examples of such are braided bimonoidal categories. We investigate
examples such as algebraic K-theory of connective complex and real topological
K-theory and Waldhausen's K-theory of spaces of the form BBG, for abelian
groups G. We show that the involution agrees with the classical one for a
bimonoidal category associated to a ring and prove that it is not trivial in
the above mentioned examples.
