Answer
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Current PowerBuilder limitations restrict the development of ArcObjects applications.
The primary limitation is that PowerBuilder requires OLE objects to support IDispatch. This limits the creation of all but a few ArcObjects.
Another limitation is the inability to "implement" an interface in PowerBuilder. This disallows the creation of custom components that fit into the ArcGIS framework.
Some basic functionality can be used in the MapControl and other controls. Again, this is severely limited by the fact that only the main interfaces, for example, IMapControl can be used and no custom interfaces can be returned and set into the members.
As a work-around, it may be possible to create wrappers in C++ or VB that would provide an IDispatch interface and call our custom interface methods internally; however, most developers would not consider this a viable work-around.