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I created a polygon in Google Earth and saved to kml. After importing as a vector layer, where the polygon crosses the prime meridian, the polygon wraps around the world.

So far, I have figured out that I need to change the projection [and offset?], but I cannot figure out how to do that.

I am new to QGIS (and GIS in general). I have already spent many hours trying to figure this out. Can somebody please help?

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Open a blank project. Go to "settings > project properties > tab Coordinate reference system" to set the coordinate reference system (CRS) of your choice.
Check 'enable on the fly projection'. Add your kml.

If you want to save the kml as a shapefile: right-click on it in the table of content and choose 'save as'. Set format to ESRI shapefile. Give it a name. Set the CRS to project CRS. And confirm. This will convert the kml to a shapefile with the right coordinate reference system.

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