pseudo-abelian category / Karoubian category in K-theory

A pseudo-abelian category or Karoubian category $mathcal{C}$ is a preaditive
category such that every idempotent morphism
$i: A to A$ in $mathcal{C}$ has a kernel and consequently a
cokernel.

Moreover the Karoubi or preudo-abelian completion
associates to an arbitrary category preadditive category
$mathcal{D}$ a pseudo-abelian category $Kar(mathcal{D})$
called the pseudo-abelian completion or Karoubian envelope of $mathcal{D}$
Here
is is shortly noted unfortunately without any references that pseudo-abelian completion
is also used in the construction of the category of pure motives, and in K-theory.

I found heaps of meterials how it is used in the
construction of the category of pure motives but almost nothing
about it’s importance in K-theory.

Can somebody give an overview of how the pseudo-abelian completion
takes important part in K-theory.