  We study the relation between the D8-branes wrapped on an orientable compact
manifold $W$ in a massive Type IIA supergravity background and the M9-branes
wrapped on a compact manifold $Z$ in a massive d=11 supergravity background
from the K-theoretic point of view. By speculating on the use of the
dimensional reduction to relate the two theories in different dimensions and by
interpreting the D8-brane charges as elements of $K_0 (C(W))$ and the
(inequivalent classes of) spaces of gauge fields on the M9-branes as the
elements of $K_0(C(Z)\times_{\bar{k}^*}G}$ a connection between charges and
gauge fields is argued to exist. This connection is realized as a map between
the corresponding algebraic K-theory groups.
