Direct Image and Index Formulas in K-Theory

Abstract

Let i : M ⊂ X be a $\overline \Gamma$-embedding of $\overline \Gamma$-manifolds. In this section, we construct the direct image mapping

$$ i_! :K_0 \left( {C_0 \left( {T^ * M} \right)_\Gamma } \right) \to K_0 \left( {C_0 \left( {T^ * X} \right)_\Gamma } \right) $$

(7.1)

and prove that it preserves the Λ-index.