In Arcmap 10 there is a menu item to create a map package and upload to Arcgis Online (File > Create Map Package > upload to...). That works fairly smoothly, if a tad slow sometimes. However once placed in system it seems the only way to access the map is to download the map package. What we really want to do is create the map in Arcmap Desktop, upload to Arcgis Online, and then embed that map in a website.
If we take exactly the same data and create the map on the website, upload the feature classes individually, apply styling and symbology using the website tools, share, and so on. The resulting map can be opened in a) Arcgis.com map viewer, b) ArcExplorer, and c) Arcmap Desktop.
In the "My Content" page a map created from Arcmap Desktop is listed as a "Map Package", and a map created entirely using the website is a "Web Map" (what we want).
Am I missing something or is this really the way it's supposed to work? If so it's a terrific duplication of effort.