### Abstract

Recent work by Baum et al. ['Expanders, exact crossed products, and the Baum-Connes conjecture', Ann. K-Theory 1(2) (2016), 155-208], further developed by Buss et al. ['Exotic crossed products and the Baum-Connes conjecture', J. reine angew. Math. 740 (2018), 111-159], introduced a crossed-product functor that involves tensoring an action with a fixed action, then forming the image inside the crossed product of the maximal-tensor-product action. For discrete groups, we give an analogue for coaction functors. We prove that composing our tensor-product coaction functor with the full crossed product of an action reproduces their tensor-crossed-product functor. We prove that every such tensor-product coaction functor is exact, and if is the action by translation on, we prove that the associated tensor-product coaction functor is minimal, thereby recovering the analogous result by the above authors. Finally, we discuss the connection with the-ization functor we defined earlier, where is a large ideal of.

Original language | English (US) |
---|---|

Journal | Journal of the Australian Mathematical Society |

DOIs | |

State | Accepted/In press - Jan 1 2020 |

### Keywords

- 2010 Mathematics subject classification
- 46L55
- 46M15

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Tensor-Product Coaction Functors'. Together they form a unique fingerprint.

## Cite this

*Journal of the Australian Mathematical Society*. https://doi.org/10.1017/S1446788720000063