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equivariant Steenrod algebra

From Hu-Kriz "Real-oriented homotopy theory and an analogue of the Adams-Novikov spectral sequence" we know about calculation of $C_2$ - equivariant Steenrod algebra. … Where can I find (if it exists) information about $(C_2)^k$-equivariant version, $k\ge 2$? I guess $k=2$ would be good enough. …
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