  We prove a colimit formula for the K-theory spectra of reductive p-adic
groups of rank one with regular coefficients in terms of the K-theory of
certain compact open subgroups. Furthermore, in the complex case, we show,
using the construction of types provided by Roche, that this result can be
improved to obtain a formula for the K-theory spectrum of every principal
series Bernstein block if the group is split.
