Help File says..."[ActiveCell] Returns a Range object that represents the active cell in the active window (the window on top) or in the specified window. If the window isn't displaying a worksheet, this property fails. Read-only... If you don't specify an object qualifier, this property returns the active cell in the active window." (Emph by me)
Try
Sheets("SheetName").Activate
Set Bereich = Application.ActiveCell.Offset(0, 1).Resize(1,4)
Too bad you can't use "Selection." That's very easy
Set Bereich = Selection.Offset(0, 1).Resize(1,4)
Troubleshooting:
MsgBox ActiveWindow.Caption 'Should be Workbook name
MsgBox ActiveCell.Parent.Name 'Sheet name
MsgBox ActiveCell.Address
Worst Case
Dim ACAdd As String
Sheets("SheetName").Activate
ACAdd = ActiveCell.Address
Set Bereich = Sheets("SheetName").Range(ACAdd).Offset(0, 1).Resize(1,4)