  We study the notion of twisted bundles on noncommutative space. Due to the
existence of projective operators in the algebra of functions on the
noncommutative space, there are twisted bundles with non-constant dimension.
The U(1) instanton solution of Nekrasov and Schwarz is such an example. As a
mathematical motivation for not excluding such bundles, we find gauge
transformations by which a bundle with constant dimension can be equivalent to
a bundle with non-constant dimension.
