I have some questionss about the construction of the complex bordism ring MU and would appreciate every answer:
I have read that the multiplication in MU is given by the tensor product of vector bundles $BU(n) \times BU(m) \rightarrow BU(n+m)$. How does this tensor product yield us a map $MU(n) \wedge MU(m) \rightarrow MU(n+m) $, I do not get how we can go from $BU$ to $MU$?
What is the unit for the multiplication on MU?
I would be happy, if you could give me an answer.