Comparing direct limit and inverse limit of even $K$-groups in non-commutative $p$-adic Lie extensions

In a previous paper of the author, we establish a duality for the direct limit and the inverse limit of higher even $K$-groups over a ${\mathbb{Z}}_p^d$-extension. In this paper, we shall establish such a duality over certain non-commutative $p$-adic Lie extensions.