For File page type objects, the file is stored as an Attachment in the CMS_Attachment table.
In the CMS_Attachment table, you can find your attachment by the AttachmentDocumentID (which in the repeater will be your DocumentID).
I would recommend using the text/xml transformation so you can leverage the macro engine if possible, and use:
{% SiteObjects.Documents.Where("DocumentID = "+DocumentID).FirstItem.AllAttachments.FirstItem.AttachmentExtension |(identity)GlobalAdministrator%}
Or just create a custom Transformation Method that performs:
CMS.DocumentEngine.AttachmentInfoProvider.GetAttachments(TheDocumentID, false).FirstObject.AttachmentExtension