Dear Inselpeter,
and it is possible that the real is a concept that exceeds itself.
You perfectly understood my concern. Any attempt to provide a closed definition of the real will lead to a contradiction or a petitio principii at some point. Yet we cannot do without the notion of the unreal, i.e. the real does have a non-empty complement.
Kant also knew that perceiving 'the' reality is not a purely passive act, but involves us applying (putting) something to it.