For compact Lie G and finite H, G/H-framed G-disc algebras are equivalent to V-framed H-disc algebras.
Lurie, Higher Topos Theory, Princeton University press, 2009
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Universal property of framed $G$-disc algebras
For compact Lie G and finite H, G/H-framed G-disc algebras are equivalent to V-framed H-disc algebras.