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The answer is to use a different document template for each language and to get YAMS to choose the correct one based on the language:
Place the document template for each language within a separate chunk. Give the chunks the names "mytemplate_id1", "mytemplate_id2", etc. where "id1", "id2" are the language group ids for the active languages.
In the document template, use the following snippet call:
[[YAMS? &get=chunk
&from=mytemplate
]]