At split boundaries, grid navigation depends on the TabAcrossSplits property as follows:

Key	Action
Left/Right Arrows	If the TabAcrossSplits property is set to True, these keys move the current cell across split boundaries to the next or previous split. If the TabAcrossSplits property is set to False (default), the behavior of these keys at split boundaries will be the same as their behavior at row boundaries. Note that a split's AllowFocus property must be True in order for these keys to move the current cell to that split.
TAB	The TAB and SHIFT+TAB keys honor TabAcrossSplits as previously described for the arrow keys.