How to convert a string to lower case in Bash?

Question

Is there a way in bash to convert a string into a lower case string?

For example, if I have:

a=\"Hi all\"

I want to convert it to:<

Answer 1

For Bash versions earlier than 4.0, this version should be fastest (as it doesn't fork/exec any commands):

function string.monolithic.tolower
{
   local __word=$1
   local __len=${#__word}
   local __char
   local __octal
   local __decimal
   local __result

   for (( i=0; i<__len; i++ ))
   do
      __char=${__word:$i:1}
      case "$__char" in
         [A-Z] )
            printf -v __decimal '%d' "'$__char"
            printf -v __octal '%03o' $(( $__decimal ^ 0x20 ))
            printf -v __char \\$__octal
            ;;
      esac
      __result+="$__char"
   done
   REPLY="$__result"
}

technosaurus's answer had potential too, although it did run properly for mee.