Time Zones in Searches

Is there a standard/commonly accepted way to search dates with time zones.

 
I am developing an application that I need to store all dates relative to
time zone.  (Using Oracle 8i as a database)
When the user enters the information, before storing it to the database, I
convert all date/times to UTC (I need a consistent/comparable date/time).
 
Now the problem, when the user is searching based on these dates
----Is it common to have the user specify a time zone relative to the
date/times on the search screen???
----Or, is it common to have the user just enter a date/time on the search
screen and return items that occurred on that date/time irregardless of time
zone???
 
Is anyone doing anything similar?  Any suggestions/comments,etc... are
welcome.