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I am giving this its own entry, not to drown it inside projective space
added the description of the equivariant K-theory ring of projective $G$-space (here).
Will give this also its own entry now, equivariant K-theory of projective G-space, for ease of hyperlinking at various related entries
added the example of infinite projective G-space (here)
and will give this a page of its own now, for ease of hyperlinking from other related pages
made the link to the classical classes of examples more explicit:
$k =$ real numbers: real projective space $\mathbb{R}P^n$
$k =$ complex numbers: complex projective space $\mathbb{C}P^n$
$k =$ quaternions: quaternionic projective space $\mathbb{H}P^n$
$k =$ octonions: octonionic projective space $\mathbb{O}P^n$
oh, sorry, wrong entry. This should have gone to projective space. Will fix.
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