Journal of the
Korean Mathematical Society JKMS

We calculate the $R(G)$-algebra structure on the reduced equivariant $K$-groups of two-dimensional spheres on which a compact Lie group $G$ acts as a reflection. In particular, the reduced equivariant $K$-groups are trivial if $G$ is abelian, which shows that the previous Y. Yang's calculation in [8] is incorrect.

Keywords: $RO(G)$-graded cohomology theory, equivariant $K$-theory, equivariant vector bundle, representation sphere

MSC numbers: Primary 19L47; Secondary 55N15, 55N25, 55N91