How to aggregate by year-month-day on a different timezone

I have a MongoDB whom store the date objects in UTC. Well, I want to perform aggregation by year,month day in a different timezone (CET).

doing this, works fine for UTC:

    BasicDBObject group_id = new BasicDBObject("_id", new BasicDBObject("year", new BasicDBObject("$year", "$tDate")).
                append("month", new BasicDBObject("$month", "$tDate")).
                append("day", new BasicDBObject("$dayOfMonth", "$tDate")).
                append("customer", "$customer"));

    BasicDBObject groupFields = group_id.
            append("eventCnt", new BasicDBObject("$sum", "$eventCnt")); 

    BasicDBObject group = new BasicDBObject("$group", groupFields);

or, if you use the command line (not tested, I only tested the java version):

{
    $group: {
        _id: {
            "year": {
                "$year", "$tDate"
            },
            "month": {
                "$month", "$tDate"
            },
            "day": {
                "$dayOfMonth", "$tDate"
            },
            "customer": "$customer"
        },
        "eventCount": {
            "$sum": "$eventCount"
        }
    }
}

How do I convert these dates into CET inside the aggregation framework?

For example '2013-09-16 23:45:00 UTC' is '2013-09-17 00:45:00 CET', this is a different day.

I'm not an expert on CET and its relation to UTC, but the following code (for the shell) should do a proper conversion (adding an hour) to a MongoDB date type:

db.dates.aggregate(
  {$project: {"tDate":{$add: ["$tDate", 60*60*1000]}, "eventCount":1, "customer":1}}
)

If you run that project command before the rest of your pipeline, the results should be in CET.