Use the Project tool with ArcObjects

Code:
   public void ReprojectSDE()
    {
      Geoprocessor gp = new Geoprocessor();
      gp.SetEnvironmentValue("workspace", @"Database Connections\StringTreeSQLExpress.sde");

      IGpEnumList files = gp.ListFeatureClasses("*", "", "");
      string file = files.Next();

      IGpEnumList dfiles = gp.ListDatasets("*", "");
      string dfile = dfiles.Next();

      while (file != "")
      {

        
        Debug.WriteLine(file);

        string f_in =  file;
        //clean up the fc file name so it does not include the chinadoll.sde part
        string f_prep = doSplit(file);
        string f_out = @"C:\temp\test.gdb\" + f_prep + "_projected";
        string sys_out = @"C:\Program Files\ArcGIS\Coordinate Systems\Projected Coordinate Systems\UTM\NAD 1983\NAD 1983 UTM Zone 11N.prj";
        string geo = "NAD_1983_To_WGS_1984_1";
        Project project = new Project();
        project.in_dataset = file;
        project.out_coor_system = sys_out;
        project.out_dataset = f_out;
        project.transform_method = geo;

        IGeoProcessorResult gpresult = gp.Execute(project, null) as IGeoProcessorResult;

        if (gpresult.MessageCount > 0)
        {

          for (int Count = 0; Count <= gpresult.MessageCount - 1; Count++)
          {

            Console.WriteLine(gpresult.GetMessage(Count));

          }

        }
        file = files.Next();
      }

      while (dfile != "")
      {
        Debug.WriteLine(dfile);
        dfile = dfiles.Next();
      }
    }

    public string doSplit(string str)
    {
      string[] ar = new string[3];
      char[] val = { '.' };
      ar = str.Split(val);
      string name = ar[2].ToString();
      return name;
    }

  }