Generalizing a construction of Luck and Oliver (9), we define a good equivariant cohomology theory on the category of proper G-CW complexes when G is an arbitrary Lie group (possibly non-compact). This is done by constructing an appropriate classifying space that arises from a G-space. It is proven that this theory effectively generalizes Segal's equivariant K- theory when G is compact.

We first construct a classifying space for defining equivariant K-theory for proper actions of discrete groups. This is then applied to construct equivariant Chern characters with values in Bredon… Expand

Abstract We prove a version of the Atiyah–Segal completion theorem for proper actions of an infinite discrete group G. More precisely, for any finite proper G-CW-complex X, K ∗ (EG× G X) is the… Expand

In a previous paper, we have constructed, for an arbitrary Lie group G and any of the fields F=R or C, a good equivariant cohomology theory KF_G^*(-) on the category of proper $G$-CW-complex and have… Expand

The purpose of this thesis is to present a fairly complete account of equivariant K-theory on compact spaces. Equivariant K-theory is a generalisation of K-theory, a rather well-known cohomology… Expand

The focus of this paper is a proof of the Nielsen-Schreier Theorem, stating that every subgroup of a free group is free, using tools from algebraic topology.