  In the present paper we consider a special class of locally trivial bundles
with fiber a matrix algebra. On the set of such bundles over a finite
$CW$-complex we define a relevant equivalence relation. The obtained stable
theory gives us a geometric description of the H-space structure $\BSU_\otimes$
on $\BSU$ related to the tensor product of virtual $\SU$-bundles of virtual
dimension 1.
