Frobenius induction for higher Whitehead groups

The theory of induced representations has served as a powerful tool in the computations of algebraic K -theory and L -theory ( [2], [7], [4, 5], [9], [10, 11, 12, 13], [14], [17], [18] ). In this paper we show how to apply this theory to obtain induction theorems for the higher Whitehead groups of Waldhausen. The same technique applies to the analogs of Whitehead groups in unitary K -theory and in L -theory. For any ring A with unit, let K ( A ) be the spectrum of the algebraic K -theory of A ([ 8 , p. 343]). Given a discrete group Γ and a subring R of the rational numbers, Loday defines a map of spectra: * where ( B Γ) is the classifying space of Γ union with a disjoint base point and R Γ is the group-ring of Γ over R .