DataGrid not updating property when using "single click" CheckBox column

I am using a Datagrid in MVVM, and I want to remove the "double click" behavior of the Standard DataGrid, which contains one Checkbox-Column (inside a DataTemplateColumn) and another two regular columns, as follows:

enter link description here

Unfortunately, the CheckBox column works fine (single click), but clicking the CheckBox is not reflected in the IsSelected property. How can this problem be solved?