Introduction Part 1. The homology of $\mathbb {Z}/p$-cell complexes with even-dimensional cells Chapter 1. Preliminaries Chapter 2. The main freeness theorem (Theorem 2.6) Chapter 3. An outline of the proof of the main freeness result (Theorem 2.6) Chapter 4. Proving the single-cell freeness results Chapter 5. Computing $ĤG_*(B \cup DV; A)$ in the key dimensions Chapter 6. Dimension-shifting long exact sequences Chapter 7. Complex Grassmannian manifolds Part 2. Observations about $RO(G)$-graded equivariant ordinary homology Chapter 8. The computation of $ĤS_*$ for arbitrary $S$ Chapter 9. Examples of $ĤS_*$ Chapter 10. $RO(G)$-graded box products Chapter 11. A weak universal coefficient theorem Chapter 12. Observations about Mackey functors