Aa,
To change the native projection of a shapefile, you need to create a new one in the projection of your choice using the SaveToProjection API. We have a Code Community project Save To Projection that deals with that scenario wiki.thinkgeo.com/wiki/Map_Suite_We...Projection
So, for your case, we will have the following code and you can see how the resulting shapefile dsiplays on Google Map:
//Code for creating new shapefile in Google Map projection from shapefile in SWEREF projection.
//Projection class to go from SWEREF 18 00 (Sweden) projection to Google Map projection (Spherical Mercator).
Proj4Projection SWEREFToGoogleMap_Projection = new Proj4Projection();
SWEREFToGoogleMap_Projection.InternalProjectionParametersString = Proj4Projection.GetEpsgParametersString(3011); //
SWEREFToGoogleMap_Projection.ExternalProjectionParametersString = Proj4Projection.GetGoogleMapParametersString(); //Google Map Projection
//Creates a new shapefile in Google Map projection from the existing shapefile in SWEREF projection.
ShapeFileFeatureLayer.SaveToProjection(@"..\..\Data\park.shp", @"..\..\Data\googlemap_park.shp", SWEREFToGoogleMap_Projection, OverwriteMode.Overwrite);
//Code for displaying the shapefile natively in Google Map projection on Google Map.
wpfMap1.MapUnit = GeographyUnit.Meter;
GoogleMapsOverlay googleMapsOverlay = new GoogleMapsOverlay();
wpfMap1.Overlays.Add(googleMapsOverlay);
ShapeFileFeatureLayer shapeFileFeatureLayer = new ShapeFileFeatureLayer(@"..\..\Data\googlemap_park.shp");
shapeFileFeatureLayer.ZoomLevelSet.ZoomLevel01.DefaultAreaStyle =
AreaStyles.CreateSimpleAreaStyle(GeoColor.FromArgb(150, GeoColor.StandardColors.Green), GeoColor.StandardColors.Black);
shapeFileFeatureLayer.ZoomLevelSet.ZoomLevel01.ApplyUntilZoomLevel = ApplyUntilZoomLevel.Level20;
LayerOverlay layerOverlay = new LayerOverlay();
layerOverlay.Layers.Add(shapeFileFeatureLayer);
wpfMap1.Overlays.Add(layerOverlay);
shapeFileFeatureLayer.Open();
wpfMap1.CurrentExtent = shapeFileFeatureLayer.GetBoundingBox();
shapeFileFeatureLayer.Close();
wpfMap1.Refresh();