Hi,

I came across the space $BU_\otimes$ when struggling with twisted K-theory. Segal proved that this is an H-space, right? I have read a dozen times by now that the group $[X, BU_\otimes]$ consists of the vector bundles of virtual dimension 1. I can clearly see the semi-group structure there, but what does the inverse of such a bundle look like?

Best regards, Ulrich Pennig