Sorry, I should make myself clear. The comboBox inside the grid already shows my object's property as defined in DisplayMemberPath. But, the real problem is that it is not "binded" to the value of the grid's column. I mean, using your example, if you have a grid displaying a list of 10 Customers, the 4th column contains the Id of the country, when entering edit mode, the combobox should display the Country with the same id as the column. If you select another Country from the Combobox, then the grid's row dataitem (Customer) should change its corresponding property value as the SelectedValue of the Combobox.
What I do have right now, is that when my cell enters edit mode, the selectedItem of the combobox is null (Displays nothing). If i open the comboboxx, whick correctly shows the items from the list, and make a selection and exit edit mode, the column shows the ToString representation of my object used in the COmbobox.