For example in Atiyah's $KR$-theory there is the notion of a Real vector bundle in contrast to complex or real vector bundles. I am also familiar with the notion of a Real $C^*$-algebra and there are probably a lot more objects with sensible definitions of Real.
However Atiyah did not use a capitalized Real in his paper "K-theory and reality", so my question is:
Whose ideas was it to write Real instead of real?
I would also be interested in the general history of this notion, but that's probably too much to ask for (judging from remarks in the above mentioned paper I suspect it starts somewhere in algebraic geometry – of which I hardly know anything.)