|Dept.||Uniwersytet Wroclawski, Poland|
I will present my recent construction of finitely generated groups containing isometrically embedded expanders. Such groups have many exotic properties: they do not embed coarsely into Hilbert space, the Baum-Connes conjecture with coefficients fails for them.
The construction allows to provide the first examples of groups that have no property A (are not exact) but still are coarsely embeddable into a Hilbert space. Even more: they act properly on CAT(0) cubical complexes. I will present some further applications of the main construction.