  Generalizing a construction of Wolfgang L\"uck and Bob Oliver, 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 Gamma-G-space.
It is proven that this theory effectively generalizes Segal's equivariant
K-theory when G is compact.
