Dear Neil, thank you for watching my problem.
I knew that the Spatial References of the Map and the Layer are not the same, this is just the reason of my question. I access the correct SpatialReference (this from the Shape) over the Interface IGeoDataset, which should show me the underlying Datasource. But the member 'Extent' of the IGeoDataset doesn't show it in the right Spat.Ref. Could this be a bug? In an older Forum-Discussion is shown also the way over the IGeoDataset. I searched the FeatureClass and the FeatureClass.FeatureDataset but can't find an envelope there.