Starting workflows in a subsite

I'm not getting this. Can someone please explain it to me?

I'm trying to start a workflow for a document and it works when the document resides in a doc library at the root site of a site collection, but not when I put a document in a doc library at a subsite of the same site collection.

This is what I did:

I've created a content type inheriting from the Document content type. I've created a workflow in SharePoint Designer and added it to my content type.

In the next step I create a document library and add the content type to this library. I add a document to the library and select my content type to be used by the document. When I pull down the context menu for the document, I can use the workflow menu option to start the workflow. So far, so good!

In my last step I create a subsite and a new document library. I set up the library and add a document exactly the same as before. When I select the context menu to start a workflow, I get "This item has no workflows to start". Why? The workflow is tied to the content type and the content type is scoped for the entire site collection, right?